topological space (Meaning)
Wordnet
topological space (n)
(mathematics) any set of points that satisfy a set of postulates of some kind
Synonyms & Antonyms of topological space
No Synonyms and anytonyms found
topological space Sentence Examples
- 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.
- 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.
- The quotient of a topological space by an equivalence relation is a topological space, with the quotient topology.
- A subset of a topological space is closed if its complement is open.
- A subset of a topological space is open if it contains a neighborhood of each of its points.
- A topological space is Hausdorff if every pair of distinct points has disjoint neighborhoods.
- A topological space is compact if every open cover has a finite subcover.
- A topological space is connected if it cannot be written as the union of two disjoint open sets.
FAQs About the word topological space
(mathematics) any set of points that satisfy a set of postulates of some kind
No synonyms found.
No antonyms found.
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.
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.
