Displaying similar documents to “Skeletally Dugundji spaces”

A spectral characterization of skeletal maps

Taras Banakh, Andrzej Kucharski, Marta Martynenko (2013)

Open Mathematics

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We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.

Spaces with fibered approximation property in dimension n

Taras Banakh, Vesko Valov (2010)

Open Mathematics

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A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: 𝕀 m × 𝕀 n → M there exists a map g′: 𝕀 m × 𝕀 n → M such that g′ is ɛ-homotopic to g and dim g′ (z × 𝕀 n) ≤ n for all z ∈ 𝕀 m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].

On van Douwen spaces and retracts of β ℕ

Alan S. Dow (2007)

Mathematica Bohemica

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Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of β ℕ . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of β ℕ expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).