�ber eine Verallgemeinerung des Borelschen Theorems

Hurewicz, Witold

doi:10.1007/bf01216792

Cited by 211 publications

(199 citation statements)

References 0 publications

Supporting

Mentioning

197

Contrasting

Unclassified

Order By: Relevance

“…Hurewicz [11] introduced this covering property and showed that for a metric space this covering property is equivalent to property E introduced by Menger [17]. In the classic literature a space with the Menger property is called a Hurewicz space.…”

Section: Introductionmentioning

confidence: 99%

Menger subsets of the Sorgenfrey line

Sakai

2009

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. A space X is said to have the Menger property if for every sequence {U n : n ∈ ω} of open covers of X, there are finite subfamilies V n ⊂ U n (n ∈ ω) such that n∈ω V n is a cover of X. Let i : S → R be the identity map from the Sorgenfrey line onto the real line and let X S = i −1 (X) for X ⊂ R. Lelek noted in 1964 that for every Lusin set L in R, L S has the Menger property. In this paper we further investigate Menger subsets of the Sorgenfrey line. Among other things, we show: (1) If X S has the Menger property, then X has Marczewski's property (s 0 ). (2) Let X be a zero-dimensional separable metric space. If X has a countable subset Q satisfying that X \ A has the Menger property for every countable set A ⊂ X \ Q, then there is an embedding e : X → R such that e(X) S has the Menger property. (3) For a Lindelöf subspace of a real GO-space (for instance the Sorgenfrey line), total paracompactness, total metacompactness and the Menger property are equivalent.

show abstract

Section: Introductionmentioning

confidence: 99%

Menger subsets of the Sorgenfrey line

Sakai

2009

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…(2) A Hurewicz space (Hurewicz, 1925) if for each sequence (U n ) n ϵ N of open covers of X there is a sequence (V n ) n ϵ N such that for each n, V n is a finite subset of U n and each xϵ X belongs to UV n for all but finitely many n; (4) A -set (Gerlits & Nagy, 1982) if for each sequence (U n ) n ϵ N of ω-covers of X there is a sequence (U n ) n ϵ N such that for each n ϵ N, U n ϵ U n and each x ϵ X belongs to U n for all but finitely many n.…”

Section: Introductionmentioning

confidence: 99%

“…(1) A Menger space (or has the Menger (covering) property) (Menger,1924), (Hurewicz, 1925) if for each sequence (U n ) n ϵ N of open covers of X there exists a sequence (V n ) n ϵ N of finite sets such that for each n ϵ N, V n is a subset of U n and U n ϵ N V n is an open cover of X;…”

Section: Introductionmentioning

confidence: 99%

A note on mappings and almost Menger and related spaces

Ljubiša¹

2016

Univ Thought

View full text Add to dashboard Cite

show abstract

“…Recall that a space X is said to have the Menger property [15], [6], [16], [8] (resp. the Rothberger property [17], [16], [18] if the selection hypothesis…”

Section: Introductionmentioning

confidence: 99%

“…In 1925 in [6] (see also [7]), W. Hurewicz introduced the Hurewicz covering property for a space X in the following way:…”

Section: Introductionmentioning

confidence: 99%