T. Kawakami

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math.LO2026

Open cell property in weakly o-minimal structures

Tomohiro Kawakami, Hiroshi Tanaka

Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem simila…

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

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…

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…

Open cell property in weakly o-minimal structures

Morse theory in definably complete d-minimal structures

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

G-invariant definable Tietze extension theorem

$G$ -invariant definable Tietze extension theorem