topological space Antonyms

No Synonyms and anytonyms found

Meaning of topological space

Wordnet

topological space (n)

(mathematics) any set of points that satisfy a set of postulates of some kind

topological space Sentence Examples

1. In mathematics, a topological space is a set endowed with a topology, which specifies the open sets in the space.
2. The topological space of real numbers with the standard topology is an example of a Euclidean space.
3. The topological space of integers with the discrete topology is an example of a discrete space.
4. The product of two topological spaces is itself a topological space, with the product topology.
5. The quotient of a topological space by an equivalence relation is a topological space, with the quotient topology.
6. A subset of a topological space is closed if its complement is open.
7. A subset of a topological space is open if it contains a neighborhood of each of its points.
8. A topological space is Hausdorff if every pair of distinct points has disjoint neighborhoods.
9. A topological space is compact if every open cover has a finite subcover.
10. A topological space is connected if it cannot be written as the union of two disjoint open sets.

FAQs About the word topological space

What is the meaning of the word topological space

(mathematics) any set of points that satisfy a set of postulates of some kind

What are the synonyms of the word topological space

No synonyms found.

What are the antonyms of the word topological space

No antonyms found.

What is the usage of word topological space

In mathematics, a topological space is a set endowed with a topology, which specifies the open sets in the space.

The topological space of real numbers with the standard topology is an example of a Euclidean space.

How to use the word topological space in a sentence?

The topological space of integers with the discrete topology is an example of a discrete space.

The product of two topological spaces is itself a topological space, with the product topology.