Zobrazeno 1 - 10
of 177
pro vyhledávání: '"Fujita Masato"'
Autor:
Fujita, Masato
We solve an open problem posed in Thamrongthanyalak's paper on the definable Banach fixed point property. A Lipschitz curve selection is a key of our solution. In addition, we show a definable version of Caristi fixed point theorem.
Externí odkaz:
http://arxiv.org/abs/2411.14661
Autor:
Fujita, Masato, Kawakami, Tomohiro
Consider a definable complete d-minimal expansion $(F, <, +, \cdot, 0, 1, \dots,)$ of an oredered field $F$. Let $X$ be a definably compact definably normal definable $C^r$ manifold and $2 \le r <\infty$. We prove that the set of definable Morse func
Externí odkaz:
http://arxiv.org/abs/2408.14675
Autor:
Fujita, Masato
There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence. In this paper, we prove this assertion and the following more general assertion: Let $\mathcal R$ be either the ordered $\mathbb R$-vect
Externí odkaz:
http://arxiv.org/abs/2408.12883
Autor:
Fujita, Masato
We propose the notions of uniform local weak o-minimality and $*$-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In this pape
Externí odkaz:
http://arxiv.org/abs/2405.06140
Autor:
Fujita, Masato
Definable topological groups whose topologies are affine have definable $\mathcal C^r$ structures in d-minimal expansions of ordered fields, where $r$ is a positive integer. We prove this fact using a new notion called partition degree of a definable
Externí odkaz:
http://arxiv.org/abs/2404.15647
Autor:
Fujita, Masato, Kawakami, Tomohiro
A $G$-invariant version of definable Tietze extension theorem for definably complete structures is proved when a definably compact definable topological group $G$ acts definably and continuously on the definable set.
Externí odkaz:
http://arxiv.org/abs/2404.00853
Autor:
Fujita, Masato
Thamrongthanyalak demonstrated a definable version of Michael's selection theorem in d-minimal expansions of the real field. We generalize this result to the case in which the structures are d-minimal expansions of ordered fields $\mathcal F=(F,<,+,\
Externí odkaz:
http://arxiv.org/abs/2402.14222
Autor:
Fujita, Masato
We consider d-minimal expansions of ordered fields. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when there is
Externí odkaz:
http://arxiv.org/abs/2311.08699
Autor:
Fujita, Masato, Kageyama, Masaru
We study quasi-quadratic modules in a pseudo-valuation domain $A$ whose strict units admit a square root. Let $\mathfrak X_R^N$ denote the set of quasi-quadratic modules in an $R$-module $N$, where $R$ is a commutative ring. It is known that there ex
Externí odkaz:
http://arxiv.org/abs/2310.04116
Autor:
Fujita, Masato
Publikováno v:
Fundamenta Mathematicae 267 (2024) , 129-156
We demonstrate that And\'ujar Guerrero, Thomas and Walsberg's results on definable compactness in o-minimal structures still hold true in definably complete locally o-minimal structures. As an application, we show that a definably simple definable to
Externí odkaz:
http://arxiv.org/abs/2303.01644