Invariant arcs, Whitney levels, and Kelley continua

Author:

van de Vel M.

Abstract

As an application of convexity in spaces of arcs, three results of a somewhat different nature have been obtained. The first one gives some simple conditions under which an arc of a semilattice is mapped back into itself by an order-preserving function. The second result states that certain Whitney levels are absolute retracts. Finally, Kelley continua are characterized by what we call approximating coselections.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference15 articles.

1. Application of a selection theorem to hyperspace contractibility;Curtis, D. W.;Canad. J. Math.,1985

2. Spaces of order arcs in hyperspaces;Eberhart, Carl;Fund. Math.,1981

3. A Compendium of Continuous Lattices

4. Whitney levels in hyperspaces of certain Peano continua;Goodykoontz, Jack T., Jr.;Trans. Amer. Math. Soc.,1982

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2. Kelley continua and the hyperspace Λ(X);Topology and its Applications;2019-10

3. Bibliography;North-Holland Mathematical Library;1993

4. A Helly property of arcs;Archiv der Mathematik;1989-03

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