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

DOI:
https://doi.org/10.1090/S0002-9947-1991-1010415-8

MathSciNet review:
1010415

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1010415-8

Keywords:
Absolute retract,
approximating coselection,
arc,
continuous selection,
convex set,
Kelley continuum,
Lawson semilattice,
Whitney map

Article copyright:
© Copyright 1991
American Mathematical Society