Atsuji has internally characterized those metric spaces $ X $ for which each real-valued
continuous function on $ X $ is uniformly continuous as follows:(1) the set $ X'$ of limit points …

This paper is devoted to introduce and study two new properties of completeness in the
setting of metric spaces. We will call them Bourbaki-completeness and cofinal …

An Atsuji space is a metric space X such that each continuous function form X to an arbitrary
metric space Y is uniformly continuous. We here present (i) characterizations of metric …

A metric space (X, d) is called an Atsuji space if every real-valued continuous function on (X,
d) is uniformly continuous. In this paper, we study twenty-five equivalent conditions for a …

This monograph, for the first time in book form, considers the large structure of metric spaces
as captured by bornologies: families of subsets that contain the singletons, that are stable …

In this section, we propose to give an application of semi-metric spaces and Mozzochi
uniformities to General Relativity. A semi-metric is a generalization of a metric; it need not …

Let< X, d> be a metric space. We find necessary and sufficient conditions on the space for
the locally Lipschitz functions to coincide with each of two more restrictive classes of locally …

Call a sequence in a metric space cofinally Cauchy if for each positive ε there exists a cofinal
(rather than residual) set of indices whose corresponding terms are ε-close. We give a …

Many years ago, S.-T. Hu gave necessary and sufficient conditions for a family of subsets of
a metrizable space X to be the family of bounded sets for some admissible metric for the …

A metric space (X, d) is called an Atsuji space if every real-valued continuous function on (X,
d) is uniformly continuous. It is well known that an Atsuji space must be complete. A metric …