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retract (Definition)

Let $ X$ be a topological space and $ Y$ a subspace of $ X$. If there exists a continuous map $ r:X \to Y$ such that $ r(y)=y$ for all $ y \in Y$, then we say $ Y$ is a retract of $ X$ and $ r$ is a retraction.



"retract" is owned by rspuzio. [ full author list (2) | owner history (1) ]
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See Also: deformation retract, period of mapping

Also defines:  retraction
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Cross-references: continuous map, subspace, topological space
There are 6 references to this entry.

This is version 2 of retract, born on 2002-02-02, modified 2004-11-11.
Object id is 1693, canonical name is Retract.
Accessed 4609 times total.

Classification:
AMS MSC: 54C15 (General topology :: Maps and general types of spaces defined by maps :: Retraction)
Pending Errata and Addenda
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