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…