$T$-convexly valued o-minimal fields are definably spherically complete

TL;DR

This paper demonstrates that T-convexly valued o-minimal fields are definably spherically complete, providing a negative answer to a specific question about expansions of valued fields by leveraging prior results.

Contribution

It establishes the definable spherical completeness of T-convexly valued o-minimal fields, extending understanding of their structural properties.

Findings

T-convexly valued o-minimal fields are definably spherically complete

Negative answer to Question 1.1 in the referenced work for certain valued field expansions

Utilizes results from arXiv:2404.07646(2) to prove the main statement

Abstract

I prove the statement in the title using results from arXiv:2404.07646(2). This shows that Question~1.1 in [1] has negative answer for certain expansions of a valued field.