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Transactions of the American Mathematical Society

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On subcategories of TOP


Authors: S. P. Franklin, D. J. Lutzer and B. V. S. Thomas
Journal: Trans. Amer. Math. Soc. 225 (1977), 267-278
MSC: Primary 54D15; Secondary 54B30
MathSciNet review: 0425894
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0425894-7
Keywords: Categorical topology, categorical characterizations
Article copyright: © Copyright 1977 American Mathematical Society