Strictly convex sets #
This file defines strictly convex sets.
A set is strictly convex if the open segment between any two distinct points lies in its interior.
A set is strictly convex if the open segment between any two distinct points lies is in its interior. This basically means "convex and not flat on the boundary".
An open convex set is strictly convex.
The translation of a strictly convex set is also strictly convex.
The translation of a strictly convex set is also strictly convex.
The translation of a strictly convex set is also strictly convex.
The preimage of a strictly convex set under an affine map is strictly convex.
The image of a strictly convex set under an affine map is strictly convex.
Alternative definition of set strict convexity, using division.
Convex sets in an ordered space #
Relates convex
and set.ord_connected
.
A set in a linear ordered field is strictly convex if and only if it is convex.
Alias of the forward direction of strict_convex_iff_ord_connected
.