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Inverse Limit of Continuous Images of Arcs

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


Puni tekst: engleski pdf 7.125 Kb

str. 47-59

preuzimanja: 247

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Sažetak

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}

Ključne riječi

Inverse system and limit, continuous image of an arc

Hrčak ID:

79056

URI

https://hrcak.srce.hr/79056

Posjeta: 381 *