Course_overview

Here I write down the definitions and theorems I want to remember for the course Algebraic Topology:

Definition(Homotopy extension property) A subspace \(A\subseteq X\) of a topological \(X\) has the homotopy extension property if for all maps \(f,g:X\to Z\) with homotopy \(H:f|_{A}\implies g\), there exists an extension of \(H\), \(H^*: f\implies g^*\).

Theorem 2.16 If \(X\) is a non-empty top then \(H_0(X;A)\cong A[\pi_0(X)]\).