Round and sleek subspaces of linear metric spaces and metric spaces

TL;DR

This paper explores properties of round and sleek subsets within linear metric spaces and metric spaces, extending previous results and identifying such subsets in subspace topologies.

Contribution

It provides new results on the structure of round and sleek subsets and their identification in subspace topologies of linear metric spaces.

Findings

Characterization of round and sleek subsets in subspace topologies

Extension of previous results on metric spaces

Identification of specific properties of these subsets

Abstract

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the present article discusses more results on such spaces along with identification of round and sleek subsets of linear metric spaces and metric spaces in the subspace topology.