Diclib.com
ChatGPT AI Dictionary

Dictionary Lookup Custom Solutions

Enter a word or phrase in any language 👆

Language:

Translation and analysis of words by ChatGPT artificial intelligence

On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:

how the word is used
frequency of use
it is used more often in oral or written speech
word translation options
usage examples (several phrases with translation)
etymology

What (who) is quotient 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

Quotient space (linear algebra)

VECTOR SPACE CONSISTING OF AFFINE SUBSETS

Linear quotient space; Quotient vector space

In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. The space obtained is called a quotient space and is denoted V/N (read "V mod N" or "V by N").

https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)

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

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)