Metrically Round and Sleek Metric Spaces

TL;DR

This paper investigates properties of round and sleek metric spaces, defining these concepts and establishing foundational results that characterize their structure and relationships within metric space theory.

Contribution

It introduces the concepts of round and sleek metric spaces and provides initial results that explore their properties and significance in metric space analysis.

Findings

Characterization of round metric spaces.

Properties of sleek metric spaces.

Relationships between open and closed balls in these spaces.

Abstract

A round metric space is the one in which closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which interior of each closed ball is the corresponding open ball. In this, article we establish some results on round metric spaces and sleek metric spaces.