Unrestricted.2016-11-142012-11-082016-11-142012-08http://hdl.handle.net/2346/47025Let 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.application/pdfengTopologyContinuum theorySpanDissertation