Covering by discrete and closed discrete sets
نویسندگان
چکیده
منابع مشابه
Covering by Discrete and Closed Discrete Sets
Say that a cardinal number κ is small relative to the space X if κ < ∆(X), where ∆(X) is the least cardinality of a non-empty open set in X . We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire σ-space and a consistent example of a normal Baire Moore space which can be covered by a small n...
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Juhasz and van Mill denote by dis(X) the least cardinal of a cover of X by discrete subspaces. They show that dis(X) ≥ c (and hence the answer to Question 1.1 is positive) for any compact crowded hereditarily normal X. In fact, this follows from their stronger result that for such X, rs(X) + ls(X) ≥ c, where rs(X) (resp., ls(X)) is the least cardinal of a cover of X by right(resp., left)-separa...
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For any space X, denote by dis(X) the smallest (infinite) cardinal κ such that κ many discrete subspaces are needed to cover X. It is easy to see that if X is any crowded (i.e. dense-in-itself) compactum then dis(X) m, where m denotes the additivity of the meager ideal on the reals. It is a natural, and apparently quite difficult, question whether in this inequality m could be replaced by c. He...
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We have already met covering spaces in Chapter 2, where our discussion was geometric and basically limited to definitions and examples. In this chapter, we return to this topic from a more algebraic point of view, which will allow us to produce numerous examples coming from group actions and to classify all covering spaces with given base (provided the latter is “nice” enough). The main tools w...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.09.009