What question did this study set out to answer?

The aim is to demonstrate that every definable G set has a definable slice at each point.

June 4, 2026Open Access

Definable slices

Key Points

The aim is to demonstrate that every definable G set has a definable slice at each point.
Consider a definably compact definable group G and a definable G set X.
Prove the existence of definable slices at every point of X.
Show that X can be covered by finitely many definable G tubes.
Every point in the definable G set X has an associated definable slice.
The set X is sufficiently structured, being covered by finitely many definable G tubes.

Abstract

Let G be a definably compact definable group and X a definable G set.We prove that there exists a definable slice at every point of X and X is covered by finitely many definable G tubes.

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Cite This Study

Tomohiro KAWAKAMI (Thu,) studied this question.

synapsesocial.com/papers/6a211549d499ed480b16e8b2 https://doi.org/https://doi.org/10.19002/an00257977.64.1

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