Displaying similar documents to “The structure of ω -limit sets for continuous maps of the interval”

On the fixed points in an ω -limit set

Jack G. Ceder (1992)

Mathematica Bohemica

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Let M and K be closed subsets of [0,1] with K a subset of the limit points of M . Necessary and sufficient conditions are found for the existence of a continuous function f : [ 0 , 1 ] → [ 0 , 1 ] such that M is an ω -limit set for f and K is the set of fixed points of f in M .

Topological characterization of the small cardinal i

Antonio de Padua Franco-Filho (2003)

Commentationes Mathematicae Universitatis Carolinae

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We show that the small cardinal number i = min { | 𝒜 | : 𝒜 is a maximal independent family} has the following topological characterization: i = min { κ ≤ c : { 0 , 1 } κ has a dense irresolvable countable subspace}, where { 0 , 1 } κ denotes the Cantor cube of weight κ . As a consequence of this result, we have that the Cantor cube of weight c has a dense countable submaximal subspace, if we assume (ZFC plus i = c ), or if we work in the Bell-Kunen model, where i = ℵ 1 and c = ℵ ω 1 .

Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

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The following statement is proved to be independent from [ LB + ¬ CH ] : ( * ) Let X be a Tychonoff space with c ( X ) ≤ ℵ 0 and π w ( X ) < ℭ . Then a union of less than ℭ of nowhere dense subsets of X is a union of not greater than π w ( X ) of nowhere dense subsets.