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May 4, 2026Collectanea mathematicaOpen Access

On spaces of arc-smooth maps

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Authors

ARArmin Rainer

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Overview

Demonstrates bornological isomorphisms in function spaces, extending arc-smooth results to closed sets with topological conditions.

Key Points

  • To explore the relationship between arc-smooth maps and function spaces with specific properties and boundaries.
  • Extended results on arc-smooth functions to closed sets with Hölder boundaries and fat subanalytic sets.
  • Proved set-theoretic identities of function spaces are bornological isomorphisms under locally convex topologies.
  • Evaluated maps into convenient vector spaces and derived corresponding exponential laws.
  • Demonstrated that arc-smooth functions maintain properties on closed sets under specific topological conditions.
  • Established that function spaces exhibit bornological isomorphisms, reinforcing the smoothness concept in higher dimensions.
  • Derived analogous results for ultradifferentiable classes related to Braun–Meise–Taylor theory.

Cite This Study

Armin Rainer (2026) studied this question.

synapsesocial.com/papers/69f836aa3ed186a739980daahttps://doi.org/10.1007/s13348-026-00510-5
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