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December 5, 2025Tatra Mountains Mathematical PublicationsOpen Access

On Borsuk’s Non-Retract Theorem

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WSWaldemar Sieg

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Overview

Analysis reveals linear extension isometry for functions in topological spaces, highlighting Borsuk's theorem on unit spheres.

Key Points

  • Unit sphere in R^n not a continuous retract of the unit closed ball, indicating its geometric properties.
  • Linear extension operator is proven to be an isometry, preserving function properties in topological spaces.
  • Analyzed piecewise continuous retracts related to Borsuk’s non-retract theorem in mathematical analysis.
  • The linear extension improves understanding of function behavior within F σ and G δ subsets across various spaces.

Cite This Study

Waldemar Sieg (2025) studied this question.

synapsesocial.com/papers/693231368e51979591dcebebhttps://doi.org/10.2478/tmmp-2025-0014
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