Revistes Catalanes amb Accés Obert (RACO)

A note on inverse limits of continuous images of arcs

I. Loncar

Resum


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 ${\mathbf X} = \{ X_{a}, p_{ab}, A\}$ is an inverse system of continuous images of arcs with monotone bonding mappings such that $\operatorname{cf} (\operatorname{card}(A))\neq \omega _{1}$, then $X = \lim {\mathbf X}$ is a continuous image of an arc if and only if each proper subsystem $\{X_{a},p_{ab},B\}$ of ${\mathbf X}$ with $\operatorname{cf}(\operatorname{card}(B)) = \omega _{1}$ has the limit which is a continuous image of an arc (Theorem 18).

Text complet: PDF