Topology, 2ed

This chapter is a review of basic mathematical concepts, beginning with set theory. One key point to keep in mind is that Munkres will occasionally disambiguate the notation $(a,b)$ as an ordered pair versus as an interval by using $a\times b$ for the latter. The text also prefers $\subset$ over $\subseteq$, emphasizing proper subsets with $\subsetneq$. I will not follow that convention in these notes.

Given a function $f:A\to B$, the text defines:

• its domain as $A$
• its range as $B$
• its image set as $f(A)$
• the restriction of $f$ to $A_0\subseteq A$, denoted $f|A_0$, as $\{(a, f(a)): a\in A_0\}$

Composites, preimages, injectivity, surjectivity, and bijectivity are all defined as usual.