Revistes Catalanes amb Accés Obert (RACO)

A note on inverse limits of continuous images of arcs

I. Loncar
DOI: 37968

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).

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