What question did this study set out to answer?

The aim is to explore the structure of definable sets within an o-minimal context, specifically focusing on orbit types and extensions.

June 4, 2026Open Access

デファイナブル固有写像と同変デファイナブルティーチェ拡張

Key Points

The aim is to explore the structure of definable sets within an o-minimal context, specifically focusing on orbit types and extensions.
Examined definable groups within an o-minimal expansion of real closed fields.
Analyzed the properties of definable G-sets to determine characteristics of orbit types.
Established the equivariant definable Tietze extension theorem for these groups.
Demonstrated that definable proper G-sets possess only finitely many orbit types.
Confirmed the equivariant definable Tietze extension theorem holds within this framework.

Abstract

Let N = (R, +, •, <, . . . ) be an o-minimal expansion of the standard structure of a real closed field R. Let G be a definable group and X a definable proper definable G set.We prove that X has only finitely many orbit types.We also prove equivariant definable Tietze extension theorem.

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