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.) |
From inside the book
Results 1-3 of 35
Page 14
... Suppose that f : SK is pressing - down ; then there are a stationary T S and an ʼn & K such that f ( a ) = n for each a ɛ T ; i.e. , f is constant on a stationary ( and therefore certainly cofinal ) set . Proof . Suppose not ; then for ...
... Suppose that f : SK is pressing - down ; then there are a stationary T S and an ʼn & K such that f ( a ) = n for each a ɛ T ; i.e. , f is constant on a stationary ( and therefore certainly cofinal ) set . Proof . Suppose not ; then for ...
Page 15
... Suppose that K is an infinite cardinal and that S is cofinal in K. Suppose further that f : Sκ has the property that f ( a ) ≥ a for each a ε S ; then there is a cofinal TS such that f ( a ) < B whenever α , βεΤ and a < β . Proof ...
... Suppose that K is an infinite cardinal and that S is cofinal in K. Suppose further that f : Sκ has the property that f ( a ) ≥ a for each a ε S ; then there is a cofinal TS such that f ( a ) < B whenever α , βεΤ and a < β . Proof ...
Page 116
... Suppose , contrariwise , that V is an X - open cover of = ɛ X with no point - finite , open refinement covering X. Let w { Sp ( V ) : V ε V } ; then W is a G ( X ) -open cover of X which has no Q - refinement in ( X ) covering X. For ...
... Suppose , contrariwise , that V is an X - open cover of = ɛ X with no point - finite , open refinement covering X. Let w { Sp ( V ) : V ε V } ; then W is a G ( X ) -open cover of X which has no Q - refinement in ( X ) covering X. For ...
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