In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all...

previously published academic journal articles Retraction (category theory) Retract (group theory) Retraction (topology) Retracted (phonetics), a sound pronounced...

of a retraction in topology: f : X → Y {\displaystyle f:X\to Y} where Y {\displaystyle Y} is a subspace of X {\displaystyle X} is a retraction in the...

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós...

Differential Topology. New York: Springer. ISBN 978-0-387-90148-0. (see p. 72–73 for Hirsch's proof utilizing non-existence of a differentiable retraction) Hilton...

the middle of the 20th century in their foundational work on algebraic topology. Category theory is used in almost all areas of mathematics. In particular...

map in the sense of the product topology and is therefore open and surjective.[citation needed] In topology, a retraction is a continuous map r: X → X which...

and in particular, every free factor, is a retract. Retraction (category theory) Retraction (topology) Baer, Reinhold (1946), "Absolute retracts in group...

) {\displaystyle f(x)=f(-x)} . Hence the theorem is correct. Define a retraction as a function h : S n → S n − 1 . {\displaystyle h:S^{n}\to S^{n-1}.}...

contractible). Furthermore, X is contractible if and only if there exists a retraction from the cone of X to X. Every contractible space is path connected and...