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.
- He used the notion of a limit point to give closure axioms to define a topological space.
- In a well-known textbook on the subject we find a continuum defined as a compact connected subset of a topological 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.’
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