On the disjoint (0,N)-cells property for homogeneous ANR's

Paweł Krupski

Displaying similar documents to “On the disjoint (0,N)-cells property for homogeneous ANR's”

Homeomorphic neighborhoods in $μ^{n + 1}$ -manifolds

Yūji Akaike (1998)

Colloquium Mathematicae

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A note on f.p.p. and $f^{*} . p . p .$

Hisao Kato (1993)

Colloquium Mathematicae

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In [3], Kinoshita defined the notion of $f^{*} . p . p .$ and he proved that each compact AR has $f^{*} . p . p .$ In [4], Yonezawa gave some examples of not locally connected continua with f.p.p., but without $f^{*} . p . p .$ In general, for each n=1,2,..., there is an n-dimensional continuum $X_{n}$ with f.p.p., but without $f^{*} . p . p .$ such that $X_{n}$ is locally (n-2)-connected (see [4, Addendum]). In this note, we show that for each n-dimensional continuum X which is locally (n-1)-connected, X has f.p.p. if and only if X has $f^{*} . p . p .$ ...

On locally $r$ -incomparable families of infinite-dimensional Cantor manifolds

Vitalij A. Chatyrko (1999)

Commentationes Mathematicae Universitatis Carolinae

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The notion of locally $r$ -incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally $r$ -incomparable families of different types of finite-dimensional Cantor manifolds.

On the generalized Massey–Rolfsen invariant for link maps

A. Skopenkov (2000)

Fundamenta Mathematicae

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For $K = K_{1} ⊔ . . . ⊔ K_{s}$ and a link map $f : K \to ℝ^{m}$ let $K^{\sim} = ⊔_{i < j} K_{i} \times K_{j}$ , define a map $f^{\sim} : K^{\sim} \to S^{m - 1}$ by $f^{\sim} (x, y) = (f x - f y) / | f x - f y |$ and a (generalized) Massey-Rolfsen invariant $α (f) \in π^{m - 1} (K)$ to be the homotopy class of $f^{\sim}$ . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps $f : K \to ℝ^{m}$ up to link concordance to $π^{m - 1} (K^{\sim})$ . If $K_{1}, . . ., K_{s}$ are closed highly homologically connected manifolds of dimension $p_{1}, . . ., p_{s}$ (in particular, homology spheres), then $π^{m - 1} (K^{\sim}) ≅ \oplus_{i < j} π_{p_{i} + p_{j} - m + 1}^{S}$ .

On a theorem of P. S. Aleksandrov

Zbigniew Karno (1997)

Colloquium Mathematicae

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The topology of the Banach–Mazur compactum

Sergey Antonyan (2000)

Fundamenta Mathematicae

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Let J(n) be the hyperspace of all centrally symmetric compact convex bodies $A \subseteq ℝ^{n}$ , n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let $J_{0} (n)$ be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) $J_{0} (2) / S O (2)$ is an Eilenberg-MacLane space $𝐊 (ℚ, 2)$ ; (4)...

On self-homeomorphic dendrites

Janusz Jerzy Charatonik, Paweł Krupski (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that for every numbers $m_{1}, m_{2} \in {3, \dots, ω}$ there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.

On the LC1-spaces which are Cantor or arcwise homogeneous

Hanna Patkowska (1993)

Fundamenta Mathematicae

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A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or $X \in L C^{1}$ is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.