Homotopy

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Definition

A homotopy from the topological spaces $(X,\mathcal{ J })$ to $(Y,\mathcal{ K })$ is a continuous function:

• $F:X\times I\rightarrow Y$ (where $I$ denotes the unit interval, $[0,1]\subseteq\mathbb{R}$)

For each $t\in I$ we have a function:

• $F_t:X\rightarrow Y$ defined by $F_t:x\mapsto F(x,t)$ - these functions, the $F_t$ are called the stages of the homotopy.

Applications

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Homotopic maps

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Conditions

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Relative homotopic maps

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Conditions

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Path homotopy

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Conditions