Displaying similar documents to “ ℵ 1 -directed inverse systems of continuous images of arcs.”

A note on inverse limits of continuous images of arcs.

Ivan Loncar (1999)

Publicacions Matemàtiques

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The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if X = {X, p, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w, then X = lim X is a continuous image of an arc if and only if each proper subsystem {X, p, B} of X with cf(card (B)) = w has the limit which is a continuous image of an arc (Theorem 18).

On open light mappings

Władysław Makuchowski (1994)

Commentationes Mathematicae Universitatis Carolinae

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Whyburn has proved that each open mapping defined on arc (a simple closed curve) is light. Charatonik and Omiljanowski have proved that each open mapping defined on a local dendrite is light. Theorem 3.8 is an extension of these results.

Local connectivity, open homogeneity and hyperspaces.

J. J. Charatonik (1993)

Revista Matemática de la Universidad Complutense de Madrid

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In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua...