The Cantor Set as an Inverse Limit of Upper Semicontinuous Functions That Are the Union of Mappings
Keywords:
Cantor set, continua, inverse limits of set valued functionsAbstract
In this paper, we study the generalized inverse limit with a single upper semi-continuous function $F$ such that it is the union of mappings from a continuum $X$ into itself. Using the concept of $\operatorname{Dom}(F)$, we show that if $X$ has the fixed point property or $X$ is an absolute neighbourhood retract (ANR) space and $\operatorname{Dom}(F)$ is a non-degenerate finite set, the generalized inverse limit is homeomorphic to the Cantor set.
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