engleski

Inverse limit of continuous images of arcs

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 – order inverse system of contonuous image of arcs such that cf(A) not equal omega 1, then X = lim X is the continuous imege of an erc (Theorem 2.17). b) b) Let X = (Xa, pab, ( A, less or equal)) 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 elements of Z there exists a countable direct subset (B, less or equal) of (A, less or equal) such that for each countable direct subset (C, less or equal) of (A, less or equal) with B subset of C the restriction hBC = pBC|lim(Wd(x,y,z),pdd1,D) of the canonical projection pBC is a homeomorphism (Theorem 2.22).

inverse system limit; continuous image of an arc

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