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Displaying similar documents to “On a compactification of the homeomorphism group of the pseudo-arc”

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 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 ∈ { 3 , ⋯ , 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.

Functions characterized by images of sets

Krzysztof Ciesielski, Dikran Dikrajan, Stephen Watson (1998)

Colloquium Mathematicae

Similarity:

For non-empty topological spaces X and Y and arbitrary families 𝒜 ⊆ 𝒫 ( X ) and ℬ ⊆ 𝒫 ( Y ) we put 𝒞 𝒜 , ℬ =f ∈ Y X : (∀ A ∈ 𝒜 )(f[A] ∈ ℬ ) . We examine which classes of functions ℱ ⊆ Y X can be represented as 𝒞 𝒜 , ℬ . We are mainly interested in the case when ℱ = 𝒞 ( X , Y ) is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class ℱ = 𝒞 (X,ℝ) is not equal to 𝒞 𝒜 , ℬ for any 𝒜 ⊆ 𝒫 ( X ) and ℬ ⊆ 𝒫 (ℝ). Thus, 𝒞 (X,ℝ) cannot be characterized by images of sets. We also show that none of the following...