H
Hajime Ishihara
Researcher at Japan Advanced Institute of Science and Technology
Publications - 85
Citations - 1073
Hajime Ishihara is an academic researcher from Japan Advanced Institute of Science and Technology. The author has contributed to research in topics: Constructive & Constructive analysis. The author has an hindex of 16, co-authored 85 publications receiving 1023 citations. Previous affiliations of Hajime Ishihara include Ludwig Maximilian University of Munich & Tokyo Institute of Technology.
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Reverse Mathematics in Bishop’s Constructive Mathematics
TL;DR: In this article, the authors overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop's constructive mathematics, especially focusing on compactness properties and continuous properties.
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Continuity Properties in Constructive Mathematics
TL;DR: It is shown that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-LacombeSchoenfield-Tsejtin theorem) and in intuitionism, which is inconsistent with CT.
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Brouwer's fan theorem and unique existence in constructive analysis
Josef Berger,Hajime Ishihara +1 more
TL;DR: A list of conditions being equivalent to FAN, such as a unique version of weak Konig's lemma, illuminates the relation between FAN and LLPO and gives a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum.
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Continuity and nondiscontinuity in constructive mathematics
TL;DR: It is shown that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that “every mapping is strongly extional”, “ every sequentially nondiscountinuous mapping issequentially continuous’, and a weak version of Markov's principle are equivalent.