Question: Which was the Byzantine Empire's last remnant to stand up against the Ottomans?
About the article "Greece", section "Medieval period (4th century–1453)".

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Medieval period (4th century–1453).
The Roman Empire in the east, following the fall of the Empire in the west in the 5th century, is conventionally known as the Byzantine Empire (but was simply called "Roman Empire" in its own time) and lasted until 1453.
With its capital in Constantinople, its language and literary culture was Greek and its religion was predominantly Eastern Orthodox Christian.
From the 4th century, the Empire's Balkan territories, including Greece, suffered from the dislocation of the "Barbarian Invasions".
The raids and devastation of the Goths and Huns in the 4th and 5th centuries and the Slavic invasion of Greece in the 7th century resulted in a dramatic collapse in imperial authority in the Greek peninsula.
Following the Slavic invasion, the imperial government retained control of only the islands and coastal areas, particularly cities such as Athens, Corinth and Thessalonica, while some mountainous areas in the interior held out on their own and continued to recognize imperial authority.
Outside of these areas, a limited amount of Slavic settlement is generally thought to have occurred, although on a much smaller scale than previously thought.
The Byzantine recovery of lost provinces began toward the end of the 8th century and most of the Greek peninsula came under imperial control again, in stages, during the 9th century.
This process was facilitated by a large influx of Greeks from Sicily and Asia Minor to the Greek peninsula, while at the same time many Slavs were captured and re-settled in Asia Minor and those that remained were assimilated.
During the 11th and 12th centuries the return of stability resulted in the Greek peninsula benefiting from strong economic growth – much stronger than that of the Anatolian territories of the Empire.
Following the Fourth Crusade and the fall of Constantinople to the "Latins" in 1204 most of Greece quickly came under Frankish rule (initiating the period known as the "Frankokratia") or Venetian rule in the case of some of the islands.
The re-establishment of the Byzantine Empire in Constantinople in 1261 was accompanied by the recovery of much of the Greek peninsula, although the Frankish Principality of Achaea in the Peloponnese remained an important regional power into the 14th century, while the islands remained largely under Genoese and Venetian control.
In the 14th century much of the Greek peninsula was lost by the Empire as first the Serbs and then the Ottomans seized imperial territory.
By the beginning of the 15th century, the Ottoman advance meant that Byzantine territory in Greece was limited mainly to the Despotate of the Morea in the Peloponnese.
After the fall of Constantinople to the Ottomans in 1453, the Morea was the last remnant of the Byzantine Empire to hold out against the Ottomans.
However, this, too, fell to the Ottomans in 1460, completing the Ottoman conquest of mainland Greece.
With the Turkish conquest, many Byzantine Greek scholars, who up until then were largely responsible for preserving Classical Greek knowledge, fled to the West, taking with them a large body of literature and thereby significantly contributing to the Renaissance.
By the time of the fall of Constantinople, the only remaining territory of the Byzantine Empire was the Despotate of the Morea (Peloponnese), which was ruled by brothers of the last Emperor, Thomas Palaiologos and Demetrios Palaiologos.
The Despotate continued on as an independent state by paying an annual tribute to the Ottomans.
Incompetent rule, failure to pay the annual tribute and a revolt against the Ottomans finally led to Mehmed II's invasion of Morea in May 1460.
Demetrios asked the Ottomans to invade and drive Thomas out.
Thomas fled.
The Ottomans moved through the Morea and conquered virtually the entire Despotate by the summer.
Demetrios thought the Morea would be restored to him to rule, but it was incorporated into the Ottoman fold.
A few holdouts remained for a time.
The island of Monemvasia refused to surrender and it was first ruled for a short time by a Catalan corsair.
When the population drove him out they obtained the consent of Thomas to place themselves under the Pope's protection before the end of 1460.
The Mani Peninsula, on the Morea's south end, resisted under a loose coalition of the local clans and then that area came under Venice's rule.
The very last holdout was Salmeniko, in the Morea's northwest.
Graitzas Palaiologos was the military commander there, stationed at Salmeniko Castle.
While the town eventually surrendered, Graitzas and his garrison and some town residents held out in the castle until July 1461, when they escaped and reached Venetian territory.
The Empire of Trebizond, which had split away from the Byzantine Empire just weeks before Constantinople was taken by the Crusaders in 1204, became the last remnant and last de facto successor state to the Byzantine Empire.
Efforts by the Emperor David to recruit European powers for an anti-Ottoman crusade provoked war between the Ottomans and Trebizond in the summer of 1461.
After a month long siege, David surrendered the city of Trebizond on 14 August 1461.
With the fall of Trebizond, the last remnant of the Roman Empire was extinguished.
The nephew of the last Emperor, Constantine XI, Andreas Palaiologos claimed to have inherited the title of Byzantine Emperor.
He lived in the Morea until its fall in 1460, then escaped to Rome where he lived under the protection of the Papal States for the remainder of his life.
Since the office of emperor had never been technically hereditary, Andreas' claim would have been without merit under Byzantine law.
However, the Empire had vanished, and Western states generally followed the Roman church sanctioned principles of hereditary sovereignty.
Seeking a life in the west, Andreas styled himself "Imperator Constantinopolitanus" ("Emperor of Constantinople"), and sold his succession rights to both Charles VIII of France and the Catholic Monarchs.
However, no one ever invoked the title after Andreas's death.
Mehmed II and his successors continued to consider themselves heirs to the Roman Empire until the demise of the Ottoman Empire in the early 20th century.
They considered that they had simply shifted its religious basis as Constantine had done before.
Meanwhile, the Danubian Principalities (whose rulers also considered themselves the heirs of the Eastern Roman Emperors) harboured Orthodox refugees, including some Byzantine nobles.
At his death, the role of the emperor as a patron of Eastern Orthodoxy was claimed by Ivan III, Grand duke of Muscovy.
He had married Andreas' sister, Sophia Paleologue, whose grandson, Ivan IV, would become the first Tsar of Russia ("tsar", or "czar", meaning "caesar", is a term traditionally applied by Slavs to the Byzantine Emperors).
Their successors supported the idea that Moscow was the proper heir to Rome and Constantinople.
The idea of the Russian Empire as the successive Third Rome was kept alive until its demise with the Russian Revolution. 
The year 1204 marks the beginning of the late Byzantine period, when probably the most important event for the Empire occurred.
Constantinople was lost for the Greek people for the first time, and the empire was conquered by Latin crusaders and would be replaced by a new Latin one, for 57 years.
In addition, the period of Latin occupation decisively influenced the empire's internal development, as elements of feudality entered aspects of Byzantine life.
In 1261 the Greek empire was divided between the former Greek Byzantine Comnenos dynasty members (Epirus) and Palaiologos dynasty (the last dynasty until the fall of Constantinople).
After the gradual weakening of the structures of the Greek Byzantine state and the reduction of its land from Turkish invasions, came the fall of the Greek Byzantine Empire, at the hands of the Ottomans, in 1453, when the Byzantine period is considered to have ended. 
By the time of the fall of Constantinople, the only remaining territory of the Byzantine Empire was the Despotate of the Morea, which was ruled by brothers of the last Emperor and continued on as a tributary state to the Ottomans.
Incompetent rule, failure to pay the annual tribute and a revolt against the Ottomans finally led to Mehmed II's invasion of Morea in May 1460; he conquered the entire Despotate by the summer.
The Empire of Trebizond, which had split away from the Byzantine Empire in 1204, became the last remnant and last "de facto" successor state to the Byzantine Empire.
Efforts by the Emperor David to recruit European powers for an anti-Ottoman crusade provoked war between the Ottomans and Trebizond in the summer of 1461.
After a monthlong siege, David surrendered the city of Trebizond on August 14, 1461.
With the fall of Trebizond, the last remnant of the Roman Empire was extinguished.
The nephew of the last Emperor, Constantine XI, Andreas Palaeologos had inherited the title of Roman Emperor.
He lived in the Morea (Peloponnese) until its fall in 1460, then escaped to Rome where he lived under the protection of the Papal States for the remainder of his life.
He styled himself "Imperator Constantinopolitanus" ("Emperor of Constantinople"), and sold his succession rights to both Charles VIII of France and the Catholic Monarchs.
However, no one ever invoked the title after Andreas's death, thus he is considered to be the last titular Roman Emperor.
Mehmed II and his successors continued to consider themselves heirs to the Roman Empire until the demise of the Ottoman Empire in the early 20th century.
Meanwhile, the Danubian Principalities (whose rulers also considered themselves the heirs of the Eastern Roman Emperors) harboured Orthodox refugees, including some Byzantine nobles.
At his death, the role of the emperor as a patron of Eastern Orthodoxy was claimed by Ivan III, Grand Duke of Muscovy.
He had married Andreas' sister, Sophia Paleologue, whose grandson, Ivan IV, would become the first Tsar of Russia ("tsar", or "czar", meaning "caesar", is a term traditionally applied by Slavs to the Byzantine Emperors).
Their successors supported the idea that Moscow was the proper heir to Rome and Constantinople.
The idea of the Russian Empire as the new, Third Rome was kept alive until its demise with the Russian Revolution of 1917. 
In 1341, the once-mighty Byzantine Empire was in a state of flux.
Despite the restoration of the Empire's capital to Constantinople and the recovery of a measure of its former power by Michael VIII Palaiologos (r. 1259–1282), the policies implemented during his reign had exhausted the state's resources, and the Empire's strength waned under his successor, Andronikos II Palaiologos (r. 1282–1328).
During Andronikos II's long reign, the remaining Byzantine possessions in Asia Minor slowly fell to the advancing Turks, most notably the newly established Ottoman emirate.
This caused a flood of refugees into Byzantium's European provinces, while at the same time the Catalan Company wrought havoc in the imperial domains.
Taxes also rose dramatically to finance tributes to the Empire's enemies.
A combination of these failures and personal ambition moved the Emperor's grandson and heir, the young Andronikos III Palaiologos, to revolt.
Supported by a group of young aristocrats led by John Kantakouzenos and Syrgiannes Palaiologos, Andronikos III deposed his grandfather after a series of conflicts during the 1320s.
Although successful in removing the old Emperor from power, the war did not augur well for the future, as the Empire's neighbours—the Serbs, Bulgarians, Turks, Genoese and Venetians—took advantage of Byzantine infighting to gain territory or expand their influence within the Empire.
The only son of a former governor of the Byzantine holdings in the Morea, John Kantakouzenos was related to the Palaiologoi through his mother.
He inherited vast estates in Macedonia, Thrace and Thessaly, and became a childhood friend and the closest and most trusted advisor of Andronikos III.
During Andronikos III's reign (1328–1341), John Kantakouzenos acted as his chief minister, holding the office of "megas domestikos", commander-in-chief of the Byzantine army.
The relationship between the two remained close, and in 1330, when the heirless Andronikos III (John V was born in 1332) fell ill he insisted that Kantakouzenos be proclaimed Emperor or regent after his death.
Their ties were further strengthened in the spring of 1341, when the latter's eldest son, Matthew Kantakouzenos, wed Irene Palaiologina, a cousin of the Emperor.
Unlike Andronikos II, who had disbanded the Byzantine army and navy, and who favoured monks and intellectuals, Andronikos III was an energetic ruler who personally led his forces in military campaigns.
In 1329, his first campaign against the Ottomans resulted in a disastrous defeat at the Battle of Pelekanos, after which the Byzantine position in Bithynia rapidly collapsed.
Subsequent sorties into the Balkans were nevertheless successful in shoring up Andronikos' tottering realm.
Thessaly and the Despotate of Epirus, two territories separated from the Empire after the Fourth Crusade, were restored to imperial rule, almost without bloodshed in 1328 and 1337 respectively.
Andronikos III also rebuilt a modest fleet, which allowed him to recover the rich and strategically placed island of Chios from the Genoese Zaccaria family in 1329 as well as to claim the allegiance of Andreolo Cattaneo, the Genoese governor of Phocaea on the Anatolian mainland.
In 1335, however, Cattaneo with Genoese assistance captured the island of Lesbos.
The Emperor led a fleet to recover it and Phocaea, and requested the aid of the Turkish emirs of Saruhan and Aydin.
Saruhan sent troops and supplies, but Aydin's ruler Umur Beg came to meet the Emperor in person.
It was during this encounter that Kantakouzenos and Umur established a long-lasting close friendship and alliance.
A war with Serbia in 1331–1334 proved less successful for the Emperor when several towns in Macedonia were captured by the Serbs, led by the renegade Syrgiannes Palaiologos.
These gains were only curtailed when the assassination of Syrgiannes and the threat of a Hungarian invasion forced the Serbian ruler, Stephen Dushan, to seek a negotiated settlement.
The subsequent peace treaty concluded between Andronikos III and Dushan was important for the future of Byzantine-Serbian relations.
For the first time, the Byzantines recognized the extensive gains the Serbs had made at the Empire's expense in the central Balkans during Andronikos II's reign.
In the aftermath of the pact, Dushan also moved his seat, and with it his realm's centre of gravity, south to Prilep.
Although the loss of Asia Minor proved irreversible, successes in Epirus and Thessaly led to a consolidation of the Empire in the Greek-speaking lands of the southern Balkans.
Andronikos III and Kantakouzenos planned further campaigns to recover the Latin principalities of southern Greece, a project of major long-term importance, for, as the historian Donald Nicol writes, "if the whole peninsula of Greece could be united under Byzantine government then the Empire would once again be a homogeneous structure, able to stand up to the Serbians, the Italians and its other enemies.
It would be small, but it would be a compact and manageable economic and administrative unit running from Cape Matapan to Thessalonica and Constantinople".