# Pure exchange economy: Set of multiple equilibria endowments

Initial endowments which can result in multiple equilibria in a pure exchange economy are explained here. Given a pure exchange economy, that is given the utility functions (which fulfil the usual properties) and total amounts of each good, what are some properties of the set of 'multiple equilibria endowment points'?
Is this set connected?
If yes, is it convex?
Are there additional properties, does a charaterization (a set of necessary and sufficient properties) exist?