Difference between revisions of "Path"
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Latest revision as of 23:47, 14 October 2016
Disambiguation
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Path may refer to:
- Path (graph) - a path in a graph or digraph is a possibly finite sequence of edges such that the final node of each edge is the initial node of the next edge.
- Path (map) (AKA: Path (function)) - A map of the form [ilmath]f:[0,1]\rightarrow X[/ilmath] for some sort of space [ilmath]X[/ilmath], where [ilmath][0,1]:=\{x\in\mathbb{R}\ \vert\ 0\le x\le 1\}\subset\mathbb{R}[/ilmath]. Continuity of the path is implied. May be smooth in some contexts. May be defined on [ilmath](-1,1)[/ilmath], [ilmath](0,1)[/ilmath], another interval or all of [ilmath]\mathbb{R} [/ilmath], the domain is (probably?) always connected.
- Path (topology) - any continuous map of the form [ilmath]f:A\rightarrow X[/ilmath] for a topological space [ilmath](X,\mathcal{ J })[/ilmath]. Where [ilmath]A[/ilmath] is a connected subset (possibly entire) of [ilmath]\mathbb{R} [/ilmath]
