Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces

Andrey V. Koldunov; Aleksandr I. Veksler

Displaying similar documents to “Maximal nowhere dense $P$ -sets in basically disconnected spaces and $F$ -spaces”

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: $i = min {κ \leq c : {0, 1}^{κ}$ 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 $c = ℵ_{ω_{1}}$ .

$d e l t a$ -sets, irresolvable and resolvable spaces

Chandan Chattopadhyay, Uttam Kumar Roy (1992)

Mathematica Slovaca

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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 $[LB + \neg CH]$ : $(*)$ Let $X$ be a Tychonoff space with $c (X) \leq ℵ_{0}$ 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.

Displaying similar documents to “Maximal nowhere dense P -sets in basically disconnected spaces and F -spaces”

Topological characterization of the small cardinal i

d e l t a -sets, irresolvable and resolvable spaces

Nowhere dense subsets and Booth's Lemma

Displaying similar documents to “Maximal nowhere dense $P$ -sets in basically disconnected spaces and $F$ -spaces”

Topological characterization of the small cardinal $i$

$d e l t a$ -sets, irresolvable and resolvable spaces