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p-pseudocompactness and related topics in topological spaces

✍ Scribed by Manuel Sanchis; Angel Tamariz-Mascarúa

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
203 KB
Volume
98
Category
Article
ISSN
0166-8641

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✦ Synopsis

We prove some basic properties of p-bounded subsets (p ∈ ω * ) in terms of z-ultrafilters and families of continuous functions. We analyze the relations between p-pseudocompactness with other pseudocompact like-properties as p-compactness and α-pseudocompactness where α is a cardinal number. We give an example of a sequentially compact ultrapseudocompact α-pseudocompact space which is not ultracompact, and we also give an example of an ultrapseudocompact totally countably compact α-pseudocompact space which is not q-compact for any q ∈ ω * , answering affirmatively to a question posed by S. García-Ferreira and Kocinac (1996). We show the distribution law cl γ (X×Y ) (A × B) = cl γ X A × cl γ Y B, where γ Z denotes the Dieudonné completion of Z, for p-bounded subsets and we generalize the classical Glisckberg Theorem on pseudocompactness in the realm of p-boundedness. These results are applied to study the degree of pseudocompactness in the product of p-bounded subsets.

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