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On Internal Characterizations of CompletelyL-Regular Spaces

✍ Scribed by Tomasz Kubiak; Marı́a Angeles de Prada Vicente

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
208 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

Complete L-regularity is internally characterized in terms of separating chains of open L-sets. A possible characterization in terms of normal and separating families of closed L-sets is discussed and it is shown that spaces admitting such families are completely L-regular. The question of whether the converse holds true remains open. Some partial solutions are however given, e.g. in the class of countably compact spaces. ᮊ 1997 Academic Press

L

, where L is a hypercontinuous lattice, in particular, a completely L w x distributive one. For these results see 17 . There are also further results, 581

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