Span of subcontinua

Let Y be continuum consisting of a ray limiting to continuum X. We prove that $\sigma (Y)\le max\{\sigma (X),\sigma 0\ast (X)\}$. 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 $YG$ such that the set of values of span of subcontinua of $YG$ is the set $G$. Some other results related to this are also presented.