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Cleavability of Manifolds
by
Abdul Mohamad
University of Auckland
Coauthors: Paul Gartside
The aim of this talk is to investigate Arhangelskii's idea of cleavability in the context of manifolds. A key role will be played by "perfectness" type properties.
The main results are the following:
Theorem. (MA(w1)) Every manifold cleavable over the class of metrisable spaces is metrisable.
Theorem. (MA(w1)) Weakly normal, perfect manifolds are metrisable.
Theorem. Weakly normal Moore manifolds are metrisable.
A space X is cleavable over a class of spaces P if, for every subset A of X, there is a continuous map, f, of X into Y Î P, such that f(A) Çf(X - A) = Æ.
A space X is weakly normal if, for every pair A and B of closed disjoint subsets of X, there is a continuous map f of X into a separable metrisable space, such that f(A) Çf(B) = Æ.
Date received: July 22, 1998
Copyright © 1998 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 # cabl-02.