Definition of topological space in English:

topological space


  • 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.

    • ‘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.’’
    • ‘Moore's regions would ultimately become open sets that form a basis for a topological space X.’
    • ‘The mathematicians in Göttingen were particularly impressed with their results on when a topological space is metrisable.’
    • ‘He used the notion of a limit point to give closure axioms to define a topological space.’
    • ‘But it is also a generalized topological space and thus provides a direct connection between logic and geometry.’
    • ‘This first work was related to their results on conditions for a topological space to be metrisable.’
    • ‘In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological space.’
    • ‘These are then applied to the topological space of the surface geometry.’
    • ‘He called this topological space the structure space of R.’
    • ‘In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space.’