Local connectivity and maps onto non-metrizable arcs
by
H. M. Tuncali
Nipissing University
Coauthors: J. Nikiel, L. B. Treybig

Three classes of locally connected continua which admit sufficiently many maps onto non-metric arcs are investigated. It is proved that all continua in those classes are continuous images of arcs and, therefore, have other quite nice properties.

We prove the following theorem.

Theorem. Let X be a locally connected continuum such that for each pair of distinct points a, b in X, there exists a continuous onto map f: X --> [c, d] such that f(a) = c and f(b) = d and [c, d] is a non-metrizable arc. If X is rim-metrizable or rim-scattered or monotonically normal, then X is a continuous image of an arc.

Date received: January 17, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-67.