engleski

A note on inverse limits of continuous images of arcs

The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if $bf X$ is an inverse system of continuous images of arcs with monotone bonding mappings such that cf(card(A))$neq omega_1$, then lim$bf X$ is a continuous image of an arc iff each proper subsystem ${;X_a, p_{;ab};, B};$ of $bf X$ with cf(card(B))=$omega_1$ has the limit which is a continuous image of an arc (Theorem 18).

inverse system and limit ; continuous image of an arc

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