Sequential cone-compactness does not imply cone-compactness

TL;DR

The paper provides a counterexample showing that sequential cone-compactness does not imply cone-compactness without the assumption of separability.

Contribution

It resolves an open problem by demonstrating the non-implication through a specific example in the non-separable case.

Findings

Sequential cone-compactness does not imply cone-compactness in non-separable spaces.

Counterexample disproves the general implication.

Addresses a previously posed open problem.

Abstract

We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.