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Definition

Homotopy

Algebraic Topology · algebraic-topology.tex
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.
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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"