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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 1745 times total.

Classification:
AMS MSC: 54D05 (General topology :: Fairly general properties :: Connected and locally connected spaces )
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