homotopy of paths

Let $X$ be a topological space and $p,q$ paths in $X$ with the same initial point $x_0$ and terminal point $x_1$. If there exists a continuous function $F:I\times I\to X$ such that

1. $F(s,0)=p(s)$ for all $s\in I$

2. $F(s,1)=q(s)$ for all $s\in I$

3. $F(0,t)=x_0$ for all $t\in I$

4. $F(1,t)=x_1$ for all $t\in I$

we call $F$ a homotopy of paths in $X$ and say $p,q$ are homotopic paths in $X$. $F$ is also called a continuous deformation.

Title	homotopy of paths
Canonical name	HomotopyOfPaths
Date of creation	2013-03-22 12:13:16
Last modified on	2013-03-22 12:13:16
Owner	RevBobo (4)
Last modified by	RevBobo (4)
Numerical id	8
Author	RevBobo (4)
Entry type	Definition
Classification	msc 55Q05
Synonym	homotopic paths
Synonym	continuous deformation
Synonym	homotopy
Related topic	HomotopyOfMaps
Related topic	HomotopyWithAContractibleDomain
Related topic	PathConnectnessAsAHomotopyInvariant