Andrew M. Bruckner, Jaroslav Smítal (1992)
Mathematica Bohemica
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We prove that every infinite nowhere dense compact subset of the interval is an -limit set of homoclinic type for a continuous function from to .
Jan van Mill (1983)
Fundamenta Mathematicae
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G. Cox (1981)
Fundamenta Mathematicae
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Fons van Engelen, Jan van Mill (1984)
Fundamenta Mathematicae
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Jan M. Jastrzębski, Jacek M. Jędrzejewski (1989)
Mathematica Slovaca
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Antonio de Padua Franco-Filho (2003)
Commentationes Mathematicae Universitatis Carolinae
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We show that the small cardinal number is a maximal independent family} has the following topological characterization: has a dense irresolvable countable subspace}, where denotes the Cantor cube of weight . As a consequence of this result, we have that the Cantor cube of weight has a dense countable submaximal subspace, if we assume (ZFC plus ), or if we work in the Bell-Kunen model, where and .