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$F_{σ}$ -absorbing sequences in hyperspaces of subcontinua

Helma Gladdines (1993)

Commentationes Mathematicae Universitatis Carolinae

Let $𝒟$ denote a true dimension function, i.e., a dimension function such that $𝒟 (ℝ^{n}) = n$ for all $n$ . For a space $X$ , we denote the hyperspace consisting of all compact connected, non-empty subsets by $C (X)$ . If $X$ is a countable infinite product of non-degenerate Peano continua, then the sequence ${(𝒟_{\geq n} (C (X)))}_{n = 2}^{\infty}$ is $F_{σ}$ -absorbing in $C (X)$ . As a consequence, there is a homeomorphism $h : C (X) \to Q^{\infty}$ such that for all $n$ , $h [{A \in C (X) : 𝒟 (A) \geq n + 1}] = B^{n} \times Q \times Q \times \dots$ , where $B$ denotes the pseudo boundary of the Hilbert cube $Q$ . It follows that if $X$ is a countable infinite product of non-degenerate...

Factorwise rigidity of embeddings of products of pseudo-arcs

Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel (2012)

Colloquium Mathematicae

An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc, then X ×...

We prove the formality property of total spaces of fat bundles over compact homogeneous spaces. Some rational homotopy obstructions to fatness are obtained.

Currently displaying 1 – 20 of 134

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Displaying 1 – 20 of 134

$F_{σ}$ -absorbing sequences in hyperspaces of subcontinua

Factorwise rigidity of embeddings of products of pseudo-arcs

Faisceaux pervers dont le support singulier est une courbe plane

Fake Lie groups and maximal tori. I.

Fake Lie groups and maximal tori. II.

Fake Lie groups and maximal tori. III.

Fake Lie groups with maximal tori. IV.

Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility

Familial 2-functors and parametric right adjoints.

Familles à un paramètre de pseudo-isotopies de plongements en codimension deux

Farrell cohomology of low genus pure mapping class groups with punctures.

Faserungen zu adjungierten Funktoren.

Fat bundles and formality

Fee Local Semigroup Constructions.

Feuilletages de variétés de dimension 3 qui sont des fibrés en cercles.

Feuilletages Proches d'une Fibration. / C. Bonatti.

Fiber maps on H-fibrations

Fibering Hilbert cube manifolds over ANRs

Fibering over the Circle within a Bordism Class.

Fiberwise shape theory.

Currently displaying 1 – 20 of 134