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connected component (Definition)

Two points $ x,y$ in a topological space $ X$ are said to be in the same connected component if there exists a subspace of $ X$ containing $ x$ and $ y$ which is connected. This relation is an equivalence relation, and the equivalence classes of $ X$ under this relation are called the connected components of $ X$.



"connected component" is owned by djao. [ full author list (2) ]
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Cross-references: equivalence classes, equivalence relation, relation, connected, subspace, connected component, topological space, points
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This is version 2 of connected component, born on 2001-11-17, modified 2002-08-22.
Object id is 948, canonical name is ConnectedComponent.
Accessed 2607 times total.

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