Euclidean neighborhood retract

In mathematics, especially algebraic topology, a Euclidean neighborhood retract or an ENR for short is a topological space that is (or homeomorphic to) a subset of a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , some n, that is a retract of some neighborhood of the subset. == Definition and results == By definition, a topological space X is called a Euclidean neighborhood retract or an ENR if there is an embedding i : X ↪ R n {\displaystyle i:X\hookrightarrow \mathbb {R} ^{n}} for some n such that i ( X ) {\displaystyle i(X)} is a retract of some neighborhood U {\displaystyle U} of it; i.e., there is a map r : U → i ( X ) {\displaystyle r:U\to i(X)} such that r | i ( X ) {\displaystyle r|_{i(X)}} is the identity (such r {\displaystyle r} is called a retraction).

Source: Wikipedia — Euclidean neighborhood retract (CC BY-SA 4.0)

Euclidean neighborhood retract

In mathematics, especially algebraic topology, a Euclidean neighborhood retract or an ENR for short is a topological space that is (or homeomorphic to) a subset of a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , some n, that is a retract of some neighborhood of the subset. == Definition and results == By definition, a topological space X is called a Euclidean neighborhood retract or an ENR if there is an embedding i : X ↪ R n {\displaystyle i:X\hookrightarrow \mathbb {R} ^{n}} for some n such that i ( X ) {\displaystyle i(X)} is a retract of some neighborhood U {\displaystyle U} of it; i.e., there is a map r : U → i ( X ) {\displaystyle r:U\to i(X)} such that r | i ( X ) {\displaystyle r|_{i(X)}} is the identity (such r {\displaystyle r} is called a retraction).

Source: Wikipedia "Euclidean neighborhood retract" · CC BY-SA 4.0

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