The category of 𝐷-completely regular spaces is simple

Heldermann, N. C.

doi:10.1090/S0002-9947-1980-0586727-1

The category of $D$-completely regular spaces is simple
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by N. C. Heldermann

Trans. Amer. Math. Soc. 262 (1980), 437-446

DOI: https://doi.org/10.1090/S0002-9947-1980-0586727-1

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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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