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A note on the Gδ-closure and the realcompactness of 2x

✍ Scribed by John Ginsburg

Publisher
Elsevier Science
Year
1976
Weight
935 KB
Volume
6
Category
Article
ISSN
0016-660X

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✦ Synopsis

In this note we describe the Gg-closure of Zx in 26x "Ising this description, we obtain the following theorem: 2x is1 Gg-closed in 2px if and on F' X is LiudeEf. An immcdiatc consequence of this result is the fact that 2x is reakomp if X is Lindelijf. Concerning the realcompactness of 2x, we show that the class of COI etely regutar spaces X, f x which 2x is realcompact, is closed und!er continuous+per losed images, In particu! ar, if X is completely regufar and 2x is realcompact, then any c tinuous-open-closed COI npletely regular image of X is reakompact.

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