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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Page 96
... new , then R n has character < K , w > for any K < 2w . 3 Lemma 7.2.5 . [ Kuz ] Let > w be regular , let R be a space of character < K , w > , and let Y be ( ∞ , k * ) - compact and countably compact ; then TRY x R R is closed . The ...
... new , then R n has character < K , w > for any K < 2w . 3 Lemma 7.2.5 . [ Kuz ] Let > w be regular , let R be a space of character < K , w > , and let Y be ( ∞ , k * ) - compact and countably compact ; then TRY x R R is closed . The ...
Page 105
... new , then ε ω , n n We may assume that for each n { V ' n ε w } # Ø [ Is ] . : ɛ n η ε ω V , ' n ' = n { Em Vn ( m ) ... new n U ( Dm n Vm ( i ) ) ] m < n i > m = n [ F U U ( D nu V ( i ) ) ] n m n new msn i > m = n [ F U ( E. ก n n new U ...
... new , then ε ω , n n We may assume that for each n { V ' n ε w } # Ø [ Is ] . : ɛ n η ε ω V , ' n ' = n { Em Vn ( m ) ... new n U ( Dm n Vm ( i ) ) ] m < n i > m = n [ F U U ( D nu V ( i ) ) ] n m n new msn i > m = n [ F U ( E. ก n n new U ...
Page 123
... New York , 1971 . [ Ju ] I. Juhász , Cardinal Functions in Topology , Mathematical Centre Tracts 34 , Mathematisch Centrum Amsterdam , 1971 . [ Ku1 ] K. Kunen , Some Comments on Box Products , preprint . [ Ku2 ] K. Kunen , Box Products ...
... New York , 1971 . [ Ju ] I. Juhász , Cardinal Functions in Topology , Mathematical Centre Tracts 34 , Mathematisch Centrum Amsterdam , 1971 . [ Ku1 ] K. Kunen , Some Comments on Box Products , preprint . [ Ku2 ] K. Kunen , Box Products ...
Common terms and phrases
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