Products of Infinite-Dimensional Spaces

Rohm, Dale M.

doi:10.2307/2047962

Cited by 9 publications

(8 citation statements)

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“…The proof that asymptotic property C is preserved by direct products of metric spaces [2,3] is based on the technique used to prove the corresponding theorem for topological property C when one of the two factors is compact [10]. The proof of the following theorem is similar in spirit to the earlier works, but the absence of a metric means that more care and bookkeeping is required.…”

Section: Resultsmentioning

confidence: 99%

Coarse direct products and property {C}

Bell¹,

Lawson²

2017

Preprint

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Section: Resultsmentioning

confidence: 99%

Coarse direct products and property {C}

Bell¹,

Lawson²

2017

Preprint

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“…Proof. Since the finite product of compact metrizable C-spaces is a C-space (see [14,Theorem 3]) and since being a C-space is invariant with respect to countable unions with closed summands (see [6, 2.24]), the space X n is a C-space for every n ∈ N + .…”

Section: κ-Discretenessmentioning

confidence: 99%

On the t-equivalence relation

Krupski¹

2013

Topology and its Applications

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For a completely regular space X, denote by C p (X) the space of continuous real-valued functions on X, with the pointwise convergence topology. In this article we strengthen a theorem of O. Okunev concerning preservation of some topological properties of X under homeomorphisms of function spaces C p (X). From this result we conclude new theorems similar to results of R. Cauty and W. Marciszewski about preservation of certain dimension-type properties of spaces X under continuous open surjections between function spaces C p (X).2010 Mathematics Subject Classification. Primary 54C35.

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“…Let X and Y be metric spaces. If X and Y have asymptotic property C, then X × Y has asymptotic property C. Theorem 1.1 is an analog of a theorem of D. M. Rohm that states that topological property C is preserved by a direct product if one of the factors is compact [27,Theorem 3]. Asymptotic property C has a compactness-like property built into the definition, which requires that the sequence of constructed families is finite.…”

Section: Introductionmentioning

confidence: 99%

On the stability of asymptotic property C for products and some group extensions

Bell

Nagórko²

2018

Algebr. Geom. Topol.

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We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if G and H are groups with asymptotic property C, then both G×H and G * H have asymptotic property C. We also prove that a group G has asymptotic property C if 1 → K → G → H → 1 is exact, if asdim K < ∞, and if H has asymptotic property C. The groups are assumed to have left-invariant proper metrics and need not be finitely generated. These results settle questions of Dydak and Virk [15], of Bell and Moran [5], and an open problem in topology in [23].2010 Mathematics Subject Classification. 54F45 (primary), 20F69 (secondary).

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Products of Infinite-Dimensional Spaces

Cited by 9 publications

References 0 publications

Coarse direct products and property {C}

Coarse direct products and property {C}

On the t-equivalence relation

On the stability of asymptotic property C for products and some group extensions

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