topological space in English

noun
1
a space that has an associated family of subsets that constitute a topology. The relationships between members of the space are mathematically analogous to those between points in ordinary two- and three-dimensional space.
He used the notion of a limit point to give closure axioms to define a topological space .

Use "topological space" in a sentence

Below are sample sentences containing the word "topological space" from the English Dictionary. We can refer to these sentence patterns for sentences in case of finding sample sentences with the word "topological space", or refer to the context using the word "topological space" in the English Dictionary.

1. The Sierpiński space is the simplest non-discrete topological space.

2. Every real or complex affine or projective space is also a topological space.

3. Homological Connectivity, a property related to the homology groups of a topological space.

4. A topological space is said to be locally Contractible if it satisfies the following equivalent conditions:

5. In order to turn a topological space into a measurable space one endows it with a σ-algebra.

6. We have Axioms of a topological space, and Axioms for a category and Axioms of groups, semigroups and cohomologies

7. Coarser definition, of or relating to a topology on a topological space whose open sets are included among the open sets of a second specified topology on the space

8. In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.

9. In topology and mathematics in general, the Boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S

10. Covering map, a function from one space to another with uniform local neighborhoods Cover (topology) , a system of (usually, open or closed) sets whose union is a given topological space Branched Covering , generalization of covers which allow for ramification

11. The category of sheaves of abelian groups on a topological space X is an abelian category, and so it makes sense to ask when a morphism f: B → C of sheaves is injective (a monomorphism) or surjective (an epimorphism).

12. In terms of the fundamental group in algebraic topology, the HNN extension is the construction required to understand the fundamental group of a topological space X that has been 'glued back' on itself by a mapping f (see e.g. Surface bundle over the circle).

13. In mathematics, a base or Basis for the topology τ of a topological space (X, τ) is a family B of open subsets of X such that every open set is equal to a union of some sub-family of B (this sub-family is allowed to be infinite, finite, or even empty).For example, the set of all open intervals in the real number line is a Basis for the Euclidean topology on because every open interval is an