Question: What was the last remnant of Byzantine Empire to hold out against 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. 
Doukas or Dukas (c. 1400 – after 1462) was a Byzantine historian who flourished under Constantine XI Palaiologos, the last Byzantine Emperor.
He is one of the most important sources for the last decades and eventual fall of the Byzantine Empire to the Ottomans. 
Following the loss of Nicomedia, the situation of the Byzantine empire remained untenable.
Unlike the Byzantine empire at 1096, the Byzantine empire now possessed very little land, save a few cities in the peloponese.
With its Serbian and Bolgarian neighbours pressing against its frontiers from the west and the Ottomans dismantling their hold on the east, the double-headed eagle of Constantinople was now truly looking in both directions at danger. 
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.