All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 66

Showing per page

On universality of countable and weak products of sigma hereditarily disconnected spaces

Taras Banakh, Robert Cauty (2001)

Fundamenta Mathematicae

Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power X ω of any subspace X ⊂ Y is not universal for the class ₂ of absolute G δ σ -sets; moreover, if Y is an absolute F σ δ -set, then X ω contains no closed topological copy of the Nagata space = W(I,ℙ); if Y is an absolute G δ -set, then X ω contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable power X ω of...

Parametrized Borsuk-Ulam problem for projective space bundles

Mahender Singh (2011)

Fundamenta Mathematicae

Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set Z f = x ∈ E | f ( x ) = 0 . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set A f = x ∈ E | f ( x ) = f ( T ( x ) ) of a fiber preserving...

Spaces with fibered approximation property in dimension n

Taras Banakh, Vesko Valov (2010)

Open Mathematics

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].

Strong Cohomological Dimension

Jerzy Dydak, Akira Koyama (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that I n d G X = d i m G X if X is a separable metric ANR and G is a countable Abelian group. Hence d i m ℤ X = d i m X for any separable metric ANR X.

The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²

J. W. Cannon, G. R. Conner (2007)

Fundamenta Mathematicae

Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...

Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin (2003)

Fundamenta Mathematicae

We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective U V n - 1 -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that d i m G X ≤ k ≤ n we have d i m G Z ≤ k and r is G-acyclic.

Currently displaying 41 – 60 of 66