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From: mkr@CS-Arthur (Mahesh K Rathi)
Newsgroups: net.math
Subject: topology and continuity.....
Message-ID: <732@CS-Arthur>
Date: Thu, 13-Sep-84 00:44:32 EDT
Article-I.D.: CS-Arthu.732
Posted: Thu Sep 13 00:44:32 1984
Date-Received: Wed, 12-Sep-84 01:49:27 EDT
References: <45@tekchips.UUCP>
Organization: Department of Computer Science, Purdue University
Lines: 19


.    Consider the lower-limit topology on R. How can we characterize
     the continuous functions when considered as functions from
     R(with usual topology) to R(with lower limit topology)?

     It may be worthwhile to note here that the concept of continuity
changes dramatically when we go from one topology to the other. For
example even the identity function on R is NOT continuous when considered
as a function from R to Rl.


NOTE:  R : set of real numbers with the usual topology
       Rl : R with the lower limit topology

       lower limit topology is the topology generated by the half-open
       intervals.