Geodesic
Separation Axioms and Direct Limits
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 337-338

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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. 
Herrlich, Horst. Separation Axioms and Direct Limits. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 337-338. doi: 10.4153/CMB-1969-043-3
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     author = {Herrlich, Horst},
     title = {Separation {Axioms} and {Direct} {Limits}},
     journal = {Canadian mathematical bulletin},
     pages = {337--338},
     year = {1969},
     volume = {12},
     number = {3},
     doi = {10.4153/CMB-1969-043-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-043-3/}
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