# Hatcher 2.1.10

Hatcher, Algebraic Topology, Chapter 2, Section 1

10. (a) Show the quotient space of a finite collection of disjoint 2-simplices obtained by identifying pairs of edges is always a surface, locally homeomorphic to $\mathbb{R}^2$. (b) Show the edges can always be oriented so as to define a $\Delta$-complex structure on the quotient surface. [This is more difficult].
Proof.

$\square$