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- Title
The legacy of Bolzano-Miranda-Poincaré intermediate value theorem.
- Authors
Kryszewski, Wojciech
- Abstract
This article is dedicated to presenting and discussing various results, including several new findings, directly or indirectly related to Bolzano's theorem, famously known as the intermediate value theorem, and its multi- or infinite-dimensional versions. We aim to provide a unified approach to these issues, consistently relying on the concept of tangency. The paper seeks to justify that tangency, a geometric property, firmly supported by appropriate topological arguments, constitutes one of the central tools in nonlinear functional analysis. Our objective is to demonstrate that the legacy of Bolzano and his followers remains significant and vibrant, constituting one of the cornerstones of contemporary mathematics.
- Subjects
NONLINEAR functional analysis; SET-valued maps; MATHEMATICS
- Publication
Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1
- ISSN
2156-8472
- Publication type
Academic Journal
- DOI
10.3934/mcrf.2024048