| 释义 |
Definition of topological space in English: topological spacenoun 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. 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 spacenountäpəˌläjəkəl 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. 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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