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Separation Axioms and Direct Limits
Published online by Cambridge University Press: 20 November 2018
Extract
A topological space X is called a direct limit of a family (Xα) of subspaces of X if and only if
(1)
(2)
If X is a direct limit of an increasing sequence (Xn) of closed subspaces then it is well known and easy to prove that X is a T1-space resp. a T4-space provided all Xn are T1-spaces resp. T4-spaces.
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- Copyright © Canadian Mathematical Society 1969
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