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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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Keywords: Developable spaces, <I>D</I>-completely regular spaces, <I>D</I>-normal spaces, epireflective hull, simple category, perfect spaces
Article copyright: © Copyright 1980 American Mathematical Society