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

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 → ℝ m let K ∼ = ⊔ i < j K i × K j , define a map f ∼ : K ∼ → S m - 1 by f ∼ ( x , y ) = ( f x - f y ) / | f x - f y | and a (generalized) Massey-Rolfsen invariant α ( f ) ∈ π m - 1 ( K ) to be the homotopy class of f ∼ . 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 → ℝ m up to link concordance to π m - 1 ( K ∼ ) . 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 ∼ ) ≅ ⊕ i < j π p i + p j - m + 1 S .

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 ⊆ 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)...