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

The legacy of Bolzano-Miranda-Poincaré intermediate value theorem.

Kryszewski, Wojciech