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Transactions of the American Mathematical Society

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Invariant arcs, Whitney levels, and Kelley continua

Author: M. van de Vel
Journal: Trans. Amer. Math. Soc. 326 (1991), 749-771
MSC: Primary 54H12; Secondary 52A01, 54B20
MathSciNet review: 1010415
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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.

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Keywords: Absolute retract, approximating coselection, arc, continuous selection, convex set, Kelley continuum, Lawson semilattice, Whitney map
Article copyright: © Copyright 1991 American Mathematical Society

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