On The Dimension Of A Topological Space
Posted: Wed Apr 13, 2016 9:28 am
Let $X$ be a topological space. Show that
- If $Y$ is any subset of $X$, then $\dim Y \leq \dim X$.
- If $ \{ U_{i} \}_{i \in I} $ is an open covering of $X$, then $\dim X = \sup \dim U_{i}$