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

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- by N. C. Heldermann PDF
- Trans. Amer. Math. Soc.
**262**(1980), 437-446 Request permission

## 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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## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**262**(1980), 437-446 - MSC: Primary 54D30; Secondary 18B30
- DOI: https://doi.org/10.1090/S0002-9947-1980-0586727-1
- MathSciNet review: 586727