On subcategories of TOP
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 by S. P. Franklin, D. J. Lutzer and B. V. S. Thomas PDF
 Trans. Amer. Math. Soc. 225 (1977), 267278 Request permission
Abstract:
A categorical characterization of a subcategory S of TOP (or ${T_2}$) is one which enables the identification of S in TOP (or ${T_2}$) without requiring the reconstruction of the topological structure of its objects. In this paper we so characterize various familiar subcategories of TOP (Hausdorff spaces, normal spaces, compact Hausdorff spaces, paracompact Hausdorff spaces, metrizable spaces, first countable spaces) in terms of the global behavior of the (objects and) morphisms of the subcategory.References

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Additional Information
 © Copyright 1977 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 225 (1977), 267278
 MSC: Primary 54D15; Secondary 54B30
 DOI: https://doi.org/10.1090/S00029947197704258947
 MathSciNet review: 0425894