This thesis discusses three distinct topics.

A topological space X is said to be self-Tietze if for every closed C ⊂ X, every continuous f : C → X admits a continuous extension F : X → X. We show that every disconnected, self-Tietze space is ultranormal. The Tychonoff Plank is an example of a compact self-Tietze space which is not completely normal, and we establish that a completely normal, zerodimensional, ...