Definition of topological space in English:

topological space

noun

Mathematics

A space which 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.
〔数〕拓扑空间
Example sentencesExamples
- These are then applied to the topological space of the surface geometry.
- A blunder occurs on page 182 when he wants to define separability of a topological space as referring to a countable base but instead says, ‘A topological space X is separable if it has a countable open covering.’
- In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological space.
- He used the notion of a limit point to give closure axioms to define a topological space.
- Moore's regions would ultimately become open sets that form a basis for a topological space X.
- In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space.
- This first work was related to their results on conditions for a topological space to be metrisable.
- He called this topological space the structure space of R.
- But it is also a generalized topological space and thus provides a direct connection between logic and geometry.
- The mathematicians in Göttingen were particularly impressed with their results on when a topological space is metrisable.

Definition of topological space in US English:

topological space

nountäpəˌläjəkəl ˈspās

Mathematics

A space which 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.
〔数〕拓扑空间
Example sentencesExamples
- In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological space.
- But it is also a generalized topological space and thus provides a direct connection between logic and geometry.
- These are then applied to the topological space of the surface geometry.
- This first work was related to their results on conditions for a topological space to be metrisable.
- A blunder occurs on page 182 when he wants to define separability of a topological space as referring to a countable base but instead says, ‘A topological space X is separable if it has a countable open covering.’
- The mathematicians in Göttingen were particularly impressed with their results on when a topological space is metrisable.
- Moore's regions would ultimately become open sets that form a basis for a topological space X.
- In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space.
- He called this topological space the structure space of R.
- He used the notion of a limit point to give closure axioms to define a topological space.

单词	topological space
释义	Definition of topological space in English: topological space noun Mathematics A space which 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. 〔数〕拓扑空间 Example sentencesExamples These are then applied to the topological space of the surface geometry. A blunder occurs on page 182 when he wants to define separability of a topological space as referring to a countable base but instead says, ‘A topological space X is separable if it has a countable open covering.’ In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological space. He used the notion of a limit point to give closure axioms to define a topological space. Moore's regions would ultimately become open sets that form a basis for a topological space X. In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space. This first work was related to their results on conditions for a topological space to be metrisable. He called this topological space the structure space of R. But it is also a generalized topological space and thus provides a direct connection between logic and geometry. The mathematicians in Göttingen were particularly impressed with their results on when a topological space is metrisable. Definition of topological space in US English: topological space nountäpəˌläjəkəl ˈspās Mathematics A space which 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. 〔数〕拓扑空间 Example sentencesExamples In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological space. But it is also a generalized topological space and thus provides a direct connection between logic and geometry. These are then applied to the topological space of the surface geometry. This first work was related to their results on conditions for a topological space to be metrisable. A blunder occurs on page 182 when he wants to define separability of a topological space as referring to a countable base but instead says, ‘A topological space X is separable if it has a countable open covering.’ The mathematicians in Göttingen were particularly impressed with their results on when a topological space is metrisable. Moore's regions would ultimately become open sets that form a basis for a topological space X. In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space. He called this topological space the structure space of R. He used the notion of a limit point to give closure axioms to define a topological space.
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