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.