Definition
Homotopy
A homotopy $h : p \simeq q$ between maps $p,q : X \to Y$ is a continuous map
\[
h: X \times I \to Y
\]
such that
\[
h(x,0) = p(x), h(x,1) = q(x)
\]
where $I = [0,1]$ the unit interval.
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
nc4860b45["Homotopy"]:::current
nd65691cf["An Example of a Homotopy"]
n34077999["Homotopy Equivalence Class"]
n9be75791["Fundamental Group"]
nc4860b45 --> nd65691cf
nc4860b45 --> n34077999
nc4860b45 --> n9be75791
click nd65691cf "../objects/d65691cf.html" "_self"
click n34077999 "../objects/34077999.html" "_self"
click n9be75791 "../objects/9be75791.html" "_self"