Relax the vector-field regularity assumptions

Relax the vector-field regularity conditions in Assumption ass:reg:X (measurability, boundedness, and local Lipschitz continuity away from the origin) as far as possible while retaining the existence of stability-preserving homotopies of semiflows and the applicability of smooth converse Lyapunov theory.

Background

Assumption ass:reg:X ensures that the Filippov regularization is upper semicontinuous and compact-convex valued, enabling the use of smooth strong Lyapunov pairs.

Example constructions show semiflows can exist even when the vector field is unbounded near the origin, motivating a search for weaker conditions that still support the main homotopy results.