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Displaying similar documents to “Conditions which ensure that a simple map does not raise dimension”

Whitney maps-a non-metric case

Janusz Charatonik, Włodzimierz Charatonik (2000)

Colloquium Mathematicae

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It is shown that there is no Whitney map on the hyperspace 2 X for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).

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 ∈ L C 1 is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.

Four mapping problems of Maćkowiak

E. Grace, E. Vought (1996)

Colloquium Mathematicae

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In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.

Composant-like decompositions

Wojciech Dębski, E. Tymchatyn (1991)

Fundamenta Mathematicae

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The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in F σ -decompositions. The second deals with the extensions of the results on accessibility in the plane.

On a compactification of the homeomorphism group of the pseudo-arc

Kazuhiro Kawamura (1991)

Colloquium Mathematicae

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A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification G P of the homeomorphism group of the pseudo-arc P, which is obtained by the...