Masato Fujita

activity

20232026

collaborators

11 papers

math.LO2026

Invariance of domain in locally o-minimal structures

Masato Fujita

Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions…

math.LO2025

Dimension functions in weakly o-minimal structures admitting strong cell decomposition

Masato Fujita

We investigate the cardinality $n_{d i m} (M)$ of the sets of dimension functions on weakly o-minimal structures $M$ admitting strong cell decomposition.

math.LO2025

Connected components in d-minimal structures

Masato Fujita

For a given d-minimal expansion $R$ of the ordered real field, we consider the expansion $R^{♮}$ of $R$ generated by the sets of the form $\bigcu…

math.LO2025

Morse functions definable in d-minimal structures

Masato Fujita

Fix a d-minimal expansion of an ordered field. We consider the space $D^{p} (M)$ of definable $C^{p}$ functions defined on a definable $C^{p}$ submanifold $M$ e…

math.LO2024

Lipchitz curve selection and its application to Thamrongthanyalak's open problem

Masato Fujita

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…

math.LO2024

Morse theory in definably complete d-minimal structures

Masato Fujita, Tomohiro Kawakami

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 $C^{r}$ manifol…

math.LO2024

Definable $C^{r}$ structures on definable topological groups in d-minimal structures

Masato Fujita

Definable topological groups whose topologies are affine have definable $C^{r}$ structures in d-minimal expansions of ordered fields, where $r$ is a positive integer. We pro…

math.LO2024

$G$ -invariant definable Tietze extension theorem

Masato Fujita, Tomohiro Kawakami

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 an…

math.LO2024

Michael's selection theorem in general d-minimal structures

Masato Fujita

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 stru…

math.LO2023

Definable quotients in d-minimal structures

Masato Fujita

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…

math.LO2023

Approximation and zero set of definable functions in a definably complete locally o-minimal structure

Masato Fujita, Tomohiro Kawakami

We consider a definably complete locally o-minimal expansion of an ordered field. We treat two topics in this paper. The first topic is a definable $C^{r}$ approximation of…

Invariance of domain in locally o-minimal structures

Dimension functions in weakly o-minimal structures admitting strong cell decomposition

Connected components in d-minimal structures

Morse functions definable in d-minimal structures

Lipchitz curve selection and its application to Thamrongthanyalak's open problem

Morse theory in definably complete d-minimal structures

Definable Cr structures on definable topological groups in d-minimal structures

G-invariant definable Tietze extension theorem

Michael's selection theorem in general d-minimal structures

Definable quotients in d-minimal structures

Approximation and zero set of definable functions in a definably complete locally o-minimal structure

Definable $C^{r}$ structures on definable topological groups in d-minimal structures

$G$ -invariant definable Tietze extension theorem