-sets in -spaces

Author:
Robert E. Atalla

Journal:
Proc. Amer. Math. Soc. **46** (1974), 125-132

MSC:
Primary 54C05; Secondary 54G05

DOI:
https://doi.org/10.1090/S0002-9939-1974-0348701-2

MathSciNet review:
0348701

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Abstract: A -set is one which is interior to any zero set which contains it. An -space may be characterized as one in which the closure of a cozero set is a -set. We study applications of -sets to the topology of -spaces, and certain set-theoretical operations under which the class of -sets is stable. A. I. Veksler has shown that in a basically disconnected space the closure of an arbitrary union of -sets is a -set, while in -spaces we are only able to prove this for countable unions. Our main result is an example of a set in the compact -space which is not a -set, but which is the closure of a union of -sets. The set is related to the almost-convergent functions of G. G. Lorentz.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0348701-2

Keywords:
-space,
basically disconnected,
extremally disconnected,
-set,
countable chain condition,
almost convergent sequence

Article copyright:
© Copyright 1974
American Mathematical Society