On Countable-Dimensional Spaces with the Menger Property, Rational Dimension and a Question of S. D. Iliadis

Pol, Elżbieta; Pol, Roman; Reńska, Mirosława

doi:10.1007/s006050050067

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…Our approach is closely related to that of [5,18,4]. (1) for every α < 2 ω the set G α is a dense G δ -set in I m(α) for some m(α) ∈ N, and for each m ∈ N,…”

Section: Michael's Concentrated Setsmentioning

confidence: 99%

“…2 Proof of Theorem 1.2. We proceed as in [18,Section 2.6]. Let S and T be the spaces described in Proposition 5.1, and let σ : K → l 2 embeds K onto a linearly independent subspace of the separable Hilbert space l 2 .…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

“…The assertion of Proposition 5.1 and a reasoning in [18], Section 2.6, yield the following: Let us notice also that this last property is equivalent to the condition that there exists a left invariant metric e on G such that (G, e) has the Haver property, cf. [3, Section 5].…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

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On metric spaces with the Haver property which are Menger spaces

Pol

2010

Topology and its Applications

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A metric space (X, d) has the Haver property if for each sequence 1 , 2 , . . . of positive numbers there exist disjoint open collections V 1 , V 2 , . . . of open subsets of X, with diameters of members of V i less than i and ∞ i=1 V i covering X, and the Menger property is a classical covering counterpart to σ -compactness. We show that, under Martin's Axiom MA, the metric square (X, d) × (X, d) of a separable metric space with the Haver property can fail this property, even if X 2 is a Menger space, and that there is a separable normed linear Menger space M such that (M, d) has the Haver property for every translation invariant metric d generating the topology of M, but not for every metric generating the topology. These results answer some questions by L. Babinkostova [L. Babinkostova, When does the Haver property imply selective screenability? Topology Appl. 154 (2007) 1971-1979; L. Babinkostova, Selective screenability in topological groups, Topology Appl. 156 (1) (2008) 2-9].

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“…Our approach is closely related to that of [5,18,4]. (1) for every α < 2 ω the set G α is a dense G δ -set in I m(α) for some m(α) ∈ N, and for each m ∈ N,…”

Section: Michael's Concentrated Setsmentioning

confidence: 99%

Section: Proof Of Theorem 12mentioning

confidence: 99%

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On metric spaces with the Haver property which are Menger spaces

Pol

2010

Topology and its Applications

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“…Another group created PLA devices that integrated silver electrodes. 155 Fabrication entailed three steps: 3DP of a portion of the device with a cut-out for the electrodes, pausing the print and screen printing and drying the Ag electrode material into the specified location, and continuing 3DP of the device. The devices fabricated in this study were used to measure the sulfide content in river and sea water.…”

Section: Fdmmentioning

confidence: 99%

Microfluidics: Innovations in Materials and Their Fabrication and Functionalization

et al. 2019

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“…Similarly, for any compactum X with rational dimension ≤ n, the parametrizations of order ≤ n + 1 with at most countably many points of order n + 1 are dense in the space of parametrizations of X on 2 ∞ (cf. [PPR,Comment 9.6]). Nevertheless, such parametrizations always form a meager set in the space of all parametrizations.…”

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confidence: 99%

On typical parametrizations of finite-dimensional compacta on the Cantor set

Milewski

2002

Fund. Math.

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Abstract. We prove that if X is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto X, the set of points of maximal order is uncountable. Moreover, if X is a perfect compactum of positive finite dimension then for a typical parametrization of X on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.

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On Countable-Dimensional Spaces with the Menger Property, Rational Dimension and a Question of S. D. Iliadis

Cited by 5 publications

References 14 publications

On metric spaces with the Haver property which are Menger spaces

On metric spaces with the Haver property which are Menger spaces

Microfluidics: Innovations in Materials and Their Fabrication and Functionalization

On typical parametrizations of finite-dimensional compacta on the Cantor set

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