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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The category of $ D$-completely regular spaces is simple


Author: N. C. Heldermann
Journal: Trans. Amer. Math. Soc. 262 (1980), 437-446
MSC: Primary 54D30; Secondary 18B30
MathSciNet review: 586727
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Abstract: In a recent paper H. Brandenburg characterized the objects of the epireflective hull of all developable spaces-that are those spaces which are homeomorphic to a subspace of a product of developable spaces-by intrinsic properties. It is shown here that these spaces, called D-completely regular, can be generated from a single second countable developable space D which has the same cardinality as the reals. As an application of this result we obtain a new characterization of D-normal spaces analogous to Urysohn's lemma and a new (external) characterization of perfect spaces (meaning every closed set is a $ {G_\delta }$).


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0586727-1
PII: S 0002-9947(1980)0586727-1
Keywords: Developable spaces, D-completely regular spaces, D-normal spaces, epireflective hull, simple category, perfect spaces
Article copyright: © Copyright 1980 American Mathematical Society