Browsing by Subject "Continuum theory"
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Item Span of subcontinua(2012-08) De-Silva, Nadeeka; Lewis, Wayne; Gelca, Razvan; Toda, Magdalena D.; Byerly, Robert E.Let Y be continuum consisting of a ray limiting to continuum X. We prove that $\sigma(Y) \leq \max \{\sigma(X), \sigma_0^{*}(X)\}$. When $\sigma(X)=0$ or when $X$ is a simple closed curve, we have that $\sigma(Y)=\sigma(X)$. Using this, we construct for each closed subset $G$ of $[0,1]$ with $0 \in G$ a one-dimensional continuum $Y_G$ such that the set of values of span of subcontinua of $Y_G$ is the set $G$. Some other results related to this are also presented.