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a e w a e y A-system analogy assume box products cf(a clearly clopen closed copy closed subset cofinal collectionwise normal compact space construct contains a closed Corollary 2.l.2 countable paracompactness countably compact countably metacompact CSEP define Definition denoted discrete union disjoint Dowker spaces Example f e F finite guarantees Hausdorff space hereditarily orthocompact homeomorphic infinite products Kunen Lemma Lemma 7.0.6 holds Let F let H n e w non-Archimedean notation 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 pseudo-compact Q-collection Q-cover Q-embedded quasi-uniformity regular cardinal resp result follows St(x stationary subset subspace suffices to show suppose Suslin tree Theorem topology uncountable w)-compact w)-metacompact weakly orthocompact X-open