Metric completion versus ideal completion

Completion of Cone Metric Spaces

In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.

The ideal completion is not sequentially adequate

It is well known that for the case of a countable partial order, the ideal completion and the chain completion coincide. We investigate the boundary at which the chain and ideal completion do not coincide. We show in particular that the ideal completion is not sequentially adequate; that is it is not possible in general to simply replace the ideal completion with a completion based on sequences...

The Completion of a Metric Space

Let (X, d) be a metric space. The goal of these notes is to construct a complete metric space which contains X as a subspace and which is the “smallest” space with respect to these two properties. The resulting space will be denoted by X and will be called the completion of X with respect to d. The hard part is that we have nothing to work with except X itself, and somehow it seems we have to p...

Constructive Metric Completion of Boolean Algebras

The Completion of Fuzzy Metric Spaces

Sherwood [Z] showed that every Menger space with continuous t-norm has a completion which is unique up to isometry. Since fuzzy metric spaces resemble in some respects probabilistic metric spaces it is to be expected that at least some fuzzy metric spaces have a completion. The purpose of this paper is to prove that. We need the following definitions. For the definition and properties of a fuzz...