Let $X$ be a completely regular space and let $T$ a topological space such that $X \subseteq T \subseteq \beta X$. Then $\beta T = \beta X$, where $\beta$ denotes the Stone-Cech compactification.

Solution: Let $f: T \mapsto [0,1]$. Then it suffices to show that the restriction of f to $X$ can be extended to $\beta X$".. 

Why is this?