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path component (Definition)

Two points $x,y$ in a topological space $X$ are said to be in the same path component if there exists a path from $x$ to $y$ in $X$ The equivalence classes of $X$ under this equivalence relation are called the path components of $X$




"path component" is owned by djao.
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Cross-references: equivalence relation, equivalence classes, path, topological space, points
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This is version 2 of path component, born on 2001-11-17, modified 2002-03-09.
Object id is 949, canonical name is PathComponent.
Accessed 2496 times total.

Classification:
AMS MSC54D05 (General topology :: Fairly general properties :: Connected and locally connected spaces )

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