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Separation Axioms and Direct Limits

Published online by Cambridge University Press:  20 November 2018

Horst Herrlich
Horst Herrlich*
Affiliation:
II. Math. InstitutFreie Universitӓt Berlin, 1 Berlin 33
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 337 - 338
Copyright
Copyright © Canadian Mathematical Society 1969