# topology
## English
### Etymology

From Late Latin topologia, from Ancient Greek τόπος (tópos, “place, locality”) + -(o)logy (“study of, a branch of knowledge”).

### Pronunciation

* (Received Pronunciation) IPA: /təˈpɒləd͡ʒi/
* (General American) IPA: /təˈpɑləd͡ʒi/
** Audio (US):(file)
* Rhymes: -ɒlədʒi

### Noun

topology (countable and uncountable, plural topologies)
* (mathematics, uncountable) The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
** 1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v,
    This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields.
** 1974 [Crane, Russak & Co.], H. Graham Flegg, From Geometry to Topology, 2001, Dover, page v,
    Many university courses in topology plunge immediately into a formalized and entirely abstract presentation of topological concepts.
* (topology) Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
    A set $X$ equipped with a topology $\tau$ is called a topological space and denoted $(X,\tau )$.
    The subsets of a set $X$ which constitute a topology are called the open sets of $X$.
** 2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43:It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on ${\widehat {V}}$ above, for the Zariski topology and the sheaf of functions $\operatorname {val} (f),f$ regular.
* (medicine) The anatomical structure of part of the body.
* (computing) The arrangement of nodes in a communications network.
* (technology) The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
* (topography) The topographical study of geographic locations or given places in relation to their history.
* (dated) The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

#### Synonyms

* (branch of mathematics): analysis situs (obsolete), geometria situs (obsolete)

#### Hypernyms

* (collection of subsets): pi-system, π-system

#### Meronyms

* open set

#### Holonyms

* topological space

#### Derived terms

* Alexandrov topology
* algebraic topology
* bus topology
* cofinite topology
* combinatorial topology
* differential topology
* discrete topology
* disjoint union topology
* ditopology
* electrotopology
* final topology
* geometric topology
* Grothendieck topology
* heterotopology
* hypertopology
* initial topology
* link topology
* mereotopology
* microtopology
* nanotopology
* network topology
* pointless topology
* point-set topology
* pretopology
* product topology
* psychotopology
* relative topology
* retopology
* ring topology
* Scott topology
* standard topology
* star topology
* subspace topology
* subtopology
* trivial topology
* Zariski topology

#### Related terms

* topological
* topologically
* topological space
* topologist

#### Translations
### See also

* homotopy
* Appendix:Glossary of topology

### Further reading

* topology on Wikipedia.Wikipedia
* Homotopy on Wikipedia.Wikipedia

### Anagrams

* optology