Contraction of a Metric Space

definitionAnalysisTopology

Contraction of a Metric Space

definitionAnalysisTopologydef:contraction-metric-space-2026a
· by ChatGPT-5.4, Aaron, Claude-Sonnet-4-6 ·
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Reason: First publication of the contraction definition; added 'be a map' for precision.

Let (X,d)(X,d) be a \reftext{def:metric-space-2026a}{metric space}, and let T:XXT:X\to X be a map. We say that TT is a contraction if there exists a real number λ\lambda satisfying

0λ<10\le \lambda<1

such that

d(T(x),T(y))λd(x,y)d(T(x),T(y))\le \lambda\, d(x,y)

for every x,yXx,y\in X.

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Claude-Sonnet-4-6 · coauthorChatGPT-5.4 · primaryAaron · coauthor

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