Examples of 'topological spaces' in a sentence
Meaning of "topological spaces"
In mathematics, topological spaces are mathematical structures that capture the concept of continuity and connectedness. They are used in topology to study properties of geometric shapes and spaces, such as their boundaries, convergence, and homotopy. Topological spaces provide a foundation for understanding and analyzing various mathematical and scientific phenomena
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- plural of topological space
How to use "topological spaces" in a sentence
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topological spaces
An orbispace is to topological spaces what an orbifold is to manifolds.
Such spaces are called finite topological spaces.
Category of topological spaces with base point.
This construction can be generalized to topological spaces.
Approximation of topological spaces by finite spaces.
Topological groups are always completely regular as topological spaces.
Any product of compact topological spaces is compact.
Topological spaces are of analytic nature.
Static systems and general topological spaces.
Finite topological spaces are a special class of finitely generated spaces.
Every constant function between topological spaces is continuous.
Some topological spaces may be endowed with a group law.
The definitions above are for arbitrary topological spaces.
Topological spaces show up naturally in almost every branch of mathematics.
Given a continuous map between two topological spaces.
See also
Ordered topological spaces and the representation of distributive lattices.
It is the terminal object in the category of topological spaces.
Of two topological spaces and.
Finding homeomorphism between topological spaces.
We know that two topological spaces are equivalent if they are homeomorphic.
Measurability and continuity for general topological spaces.
Topological spaces in fact lead to very special topoi called locales.
Singular homology is a useful invariant of topological spaces up to homotopy equivalence.
The attaching construction is an example of a pushout in the category of topological spaces.
Locally compact topological spaces.
Examples of topological spaces that fail to be compactly generated include the following.
This has absolutely no equivalent in the realm of topological spaces.
Graphs as topological spaces.
Homotopy groups are such a way of associating groups to topological spaces.
Hausdorff spaces are topological spaces in which individual points have disjoint neighborhoods.
Thus one has the category of topological spaces and.
In topological spaces.
Young measures on topological spaces.
Linear topological spaces are complete in finite dimension but generally incomplete in infinite dimension.
This definition can also be extended to metric and topological spaces.
A homeomorphism between topological spaces induces a natural isomorphism between their fundamental groups.
It characterizes distributive lattices as the lattices of compact open sets of certain topological spaces.
All spaces in this glossary are assumed to be topological spaces unless stated otherwise.
This construction makes all sheaves into representable functors on certain categories of topological spaces.
Topological manifolds form an important class of topological spaces with applications throughout mathematics.
Connectedness is one of the principal topological properties that are used to distinguish topological spaces.
The construction serves to replace any map of topological spaces by a homotopy equivalent cofibration.
Especially this includes all locales and hence all open set lattices of topological spaces.
A continuous map between two topological spaces induces a group homomorphism between the associated homotopy groups.
A topological group is a group object in the category of topological spaces with continuous functions.
Two topological spaces carrying the trivial topology are homeomorphic iff they have the same cardinality.
This theorem is extremely powerful for showing that two topological spaces are not homeomorphic.
Paracompact topological spaces are spaces for which every open cover contains a locally finite open refinement.
Let Top be the category of all topological spaces.
Topological spaces having this covering property are called Menger spaces.
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Examples of using Topological
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An orbispace is to topological spaces what an orbifold is to manifolds
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Topological defects in nematic droplets of hard spherocylinders
