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Some Generalizations of Pseudocompactness
Author(s) -
GARCÍAFERREIRA SALVADOR
Publication year - 1994
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1994.tb44130.x
Subject(s) - compact space , mathematics , order (exchange) , type (biology) , space (punctuation) , pure mathematics , cardinal number (linguistics) , combinatorics , discrete mathematics , computer science , biology , philosophy , ecology , finance , economics , operating system , linguistics
In this paper, we introduce the concepts of p ‐boundedness for p ɛω*, (α, M )‐pseudocompactness and (α, M )‐compactness, for a cardinal number α and Ø≠ M ⊆β(ω)\ω. We prove that X α is pseudocompact (respectively, countably compact) iff X is (α, M )‐pseudocompact (respectively, (α, M )‐compact), for some Ø≠ M ⊆β(ω)\ω; the Rudin‐Keisler order on β(ω)\ω can be defined in terms of p ‐boundedness and p ‐pseudocompactness; and if p ɛβ(ω)\ω then p is RK ‐minimal (selective) iff the space ω∪ T(p) is p ‐pseudocompact, where T(p) is the type of p in β(ω)\ω.