Original scientific paper

Inverse Limit of Continuous Images of Arcs

Ivan Lončar ; Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia

Abstract

The main purpose of this paper is to study the inverse limits of continuous image of arcs. We shall prove: a) If X = {Xa, Pab, A}is a monotone well- ordered inverse system of continuous image of arcs such that cf(A)≠ ω1, then X = limX is the continuous image of an arc (Theorem 2.17). b) Let X = {Xa, Pab, (A,≤)} be an inverse system of continuous image of arcs with monotone surjective bonding mappings. Then X = limX is the continuous image of an arc if and only if for each cyclic element Z of X and the points x, y, z∈Z there exists a countable directed subset (B,≤)of (A,≤) such that for each countable directed subset (C,≤)of (A,≤)with C⊇B the restriction hBc = Pbc|lim{Wd(x,y,z),Pdd1,D} of the canonical projection Pbc is a homeomorphism hBC : lim{Wd(x,y,z),Pdd1,D} --> lim{Wc(x, y, z),Pcc1, C}

Keywords

Inverse system and limit; continuous image of an arc

Hrčak ID:

79056

URI

https://hrcak.srce.hr/79056

Publication date:

12.12.1997.

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