Homotopy
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Contents
Definition
A homotopy from the topological spaces [ilmath](X,\mathcal{ J })[/ilmath] to [ilmath](Y,\mathcal{ K })[/ilmath] is a continuous function[1][2]:
- [ilmath]F:X\times I\rightarrow Y[/ilmath] (where [ilmath]I[/ilmath] denotes the unit interval, [ilmath][0,1]\subseteq\mathbb{R} [/ilmath])
For each [ilmath]t\in I[/ilmath] we have a function:
- [ilmath]F_t:X\rightarrow Y[/ilmath] defined by [ilmath]F_t:x\mapsto F(x,t)[/ilmath] - these functions, the [ilmath]F_t[/ilmath] are called the stages[1] of the homotopy.
Applications
References
- ↑ 1.0 1.1 Algebraic Topology - Homotopy and Homology - Robert M. Switzer
- ↑ Introduction to Topology - Theodore W. Gamelin & Robert Everist Greene
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