A note on inverse limits of continuous images of arcs

• Autores: Ivan Loncar
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 43, Nº 2, 1999, págs. 485-499
• Idioma: inglés
• DOI: 10.5565/publmat_43299_03
• Títulos paralelos:
  • Una nota sobre límites inversos de imágenes continuas de arcos
• Enlaces
  • Texto completo
• Resumen

  • 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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