Arcwise connected and hereditarily smooth continua
نویسندگان
چکیده
منابع مشابه
Hereditarily Weakly Confluent Mappings onto S
Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...
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For a hereditarily unicoherent continuum X, its kernel means the common part of all subcontinua of X that intersect all arc components of X. This concept naturally appears when absolute retracts for the class of hereditarily unicoherent continua are studied. Let Y be such an absolute retract. Among other results, we prove that (a) Y is indecomposable if and only if it is identical with its kern...
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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...
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A continuum means comp6lct, connected metric space. A hereditarily unicoherent and arcwise connected continuum is called a dendroid. It follows that it is hereditarily decomposable ([2], (47), p. 239). A hereditarily unicoherent and hereditarily decomposable continuum is said to be a A.-dendroid. Thus, every dendroid is a }.-dendroid and an arcwise connected A.-dendroid is a dendroid. Note that...
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Let G be the family of nite collections S where S is a collection of closed, bounded, arcwise connected sets in R 2 which for any S; T 2 S where S \ T 6 = ;, it holds that S \ T is arcwise connected. Given S 2 G which is triangle-free, we show that provided S is suu-ciently large there exists a subcollection S 0 S of at most 5 sets with the property that the sets of S surrounded by S 0 induce a...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1976
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-92-2-149-171