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On dimensionally restricted maps

H. Murat Tuncali, Vesko Valov (2002)

Fundamenta Mathematicae

Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an F σ -subset A k of X such that d i m A k ≤ k and the restriction f | ( X ∖ A k ) is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about...

On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum S n , α , β such that (a) d i m S n , α , β = n ; (b) t r D g S n , α , β = t r D g o S n , α , β = α ; (c) t r i n d S n , α , β = t r I n d ₀ S n , α , β = β ; (d) if β < ω(⁺), then S n , α , β is separable and first countable; (e) if n = 1, then S n , α , β can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then S n , α , β can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then S n , α , β can be made chainable and hereditarily indecomposable. In particular,...

On Eberlein compactifications of metrizable spaces

Takashi Kimura, Kazuhiko Morishita (2002)

Fundamenta Mathematicae

We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.

Currently displaying 61 – 80 of 245