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Etymologie

Was (wer) ist identification topology - definition

TOPOLOGICAL SPACE CONSISTING OF EQUIVALENCE CLASSES OF POINTS IN ANOTHER TOPOLOGICAL SPACE

Quotient topology; Quotient (topology); Quotient map; Identification space; Identification map; Quotient topological space; Gluing (topology); Identifiation map; Hereditarily quotient map

$For example, <math>[0,1]/\{0,1\}</math> is homeomorphic to the circle <math>S^1.</math>$

Trivial topology

TOPOLOGY WHERE THE ONLY OPEN SETS ARE THE EMPTY SET AND THE ENTIRE SPACE

Indiscrete topology; Indiscrete space; Codiscrete topology

In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly called indiscrete, anti-discrete, concrete or codiscrete.

https://en.wikipedia.org/wiki/Trivial_topology

Computational topology

SUBFIELD OF TOPOLOGY WITH AN OVERLAP WITH AREAS OF COMPUTER SCIENCE

Algorithmic topology

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.

https://en.wikipedia.org/wiki/Computational_topology

Étale topology

GROTHENDIECK TOPOLOGY ON THE CATEGORY OF SCHEMES, WHOSE COVERING FAMILIES ARE JOINTLY SURJECTIVE FAMILIES OF ÉTALE MORPHISMS

Etale topology; Étale sheaf

In algebraic geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic. The étale topology was originally introduced by Grothendieck to define étale cohomology, and this is still the étale topology's most well-known use.

https://en.wikipedia.org/wiki/Étale_topology

Wikipedia

Quotient space (topology)

In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words, a subset of a quotient space is open if and only if its preimage under the canonical projection map is open in the original topological space.

Intuitively speaking, the points of each equivalence class are identified or "glued together" for forming a new topological space. For example, identifying the points of a sphere that belong to the same diameter produces the projective plane as a quotient space.

https://en.wikipedia.org/wiki/Quotient space (topology)