Loop (topology)

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  1. Don't be lazy, give full definition
Note: see loop for other uses of the term.


Let [ilmath]p:[0,1]\rightarrow X[/ilmath] be a path exactly as is defined on that page, then[1]:

  • [ilmath]p[/ilmath] is a loop if[Note 1]:
    • [ilmath]p(0)=p(1)[/ilmath], or in words: the initial point equals the terminal point of the path.

We call [ilmath]p(0)=p(1)=x_0[/ilmath] the base point of the loop.

The constant loop based at [ilmath]x_0\in X[/ilmath] is the loop: [ilmath]\ell:[0,1]\rightarrow X[/ilmath] given by [ilmath]\ell:t\mapsto x_0[/ilmath]

See also


  1. See also: Definitions and iff


  1. Introduction to Topological Manifolds - John M. Lee