F: X × [0,1] → Y
H_n(X) = ker(∂ n) / im(∂ {n+1})
In Switzer's text, homotopy is introduced as a way of relating maps between topological spaces. Specifically, Switzer defines homotopy as a continuous map: switzer algebraic topology homotopy and homology pdf
... → C_n → C_{n-1} → ... → C_1 → C_0 → 0 F: X × [0,1] → Y H_n(X) =
Homotopy is a fundamental concept in algebraic topology that describes the continuous deformation of one function into another. In essence, homotopy is a way of measuring the similarity between two functions. Two functions are said to be homotopic if one can be continuously deformed into the other without leaving the space. F: X × [0