The Behavior of Orthocompactness in Products, with Emphasis on Certain Analogies with that of Normality Under Similar Circumstances, Or Orthocompact: Metacompact - Normal - Paracompact (a.E.) |
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a x ß A-System analogy assume base box products cf(a cf(B cf(k Chapter clearly clopen closed copy closed subset cofinal collectionwise normal compact space construct contains a closed Corollary countably compact countably metacompact CSEP D₂ define Definition discrete union Dowker spaces Example F is s.d. finite guarantees Hausdorff Hausdorff space hereditarily orthocompact homeomorphic infinite products Kunen Lemma Lemma 7.0.6 holds let H Morita's non-Archimedean numbers obviously open cover open nbhd open refinement open sets open subset ord(x ortho orthocompact iff orthocompact space orthocompactness and normality P-type point-finite precisely-indexed products of ordinals Proposition 2.1.4 pseudo-compact Q-collection Q-cover Q-embedded Q-refinement quasi-uniformity regular cardinal resp result follows St(x stationary subset subspace suffices to show Suppose Suslin tree T₁ Theorem uncountable w)-compact w)-metacompact w)-paracompactness w₁ weakly orthocompact X-open α α αελ ε μ ε ω ελ εω