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From: mkr@CS-Arthur (Mahesh K Rathi)
Newsgroups: net.math
Subject: locally finite family of sets and continuity....
Message-ID: <733@CS-Arthur>
Date: Thu, 13-Sep-84 00:58:19 EDT
Article-I.D.: CS-Arthu.733
Posted: Thu Sep 13 00:58:19 1984
Date-Received: Wed, 12-Sep-84 01:50:00 EDT
References: <45@tekchips.UUCP>
Organization: Department of Computer Science, Purdue University
Lines: 18


     Let X and Y be two sets and let f be a function from X to Y.

     Let { A(index) } be a family of subsets of X (indexed over some
possibly uncountable set) which cover X i.e. union of the sets in this
class equal X. Also suppose that f is continuous when restricted to any
of the sets in the given family.


     Prove that if the given family of subsets is LOCALLY FINITE and
if each of the subsets in the family is CLOSED then f is continuous.


Def: An indexed family of subsets of X is said to be LOCALLY FINITE
     if each point x in X has a neighborhood that intersects only
     finitely many subsets in the family.