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