International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 2, Pages 109-119
doi:10.1155/S016117120000363X
ℵ1-directed inverse systems of continuous images of arcs
Faculty of Organization and Informatics, Pavlinska 2, Varaždin, Croatia
Received 8 July 1999
Copyright © 2000 Ivan Lončar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The main purpose of this paper is to prove that if X={Xa,pab,A} is a usual ℵ1-directed inverse system
of continuous images of arcs with monotone bonding mappings, then
X=limX is a continuous image of an arc
(Theorem 2.4). Some applications of this statement are also
given.