# A note on quasi-metric spaces

@article{Albert1941ANO, title={A note on quasi-metric spaces}, author={George E. Albert}, journal={Bulletin of the American Mathematical Society}, year={1941}, volume={47}, pages={479-482} }

In the present note it is shown that a very useful generalized distance function may be defined in certain of these spaces. Clearly, any such distance function must be an asymmetric one. W. A. Wilson considered the definition of asymmetric distances in certain spaces which satisfy stronger separation axioms than K. I t is shown here that a slight modification of one of the axioms in [W] allows the extension of a large part of the theory developed there to spaces subject to K. Since many of the… Expand

#### 28 Citations

Some Results on Exhaustiveness in Asymmetric Metric Spaces

- Mathematics
- 2015

We introduce here the notion of exhaustiveness, which is related with the notion of equicon- tinuity, in asymmetric metric spaces. We give the relation between equicontinuity and exhaustiveness in… Expand

Convexity and quasi-uniformizability of closed preordered spaces

- Mathematics, Physics
- 2013

Abstract In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions.… Expand

A CONSTRUCTION OF A QUASI-METRIC SOUSLIN SPACE WITH A POINT-COUNTABLE BASE

- Mathematics
- 1977

Publisher Summary This chapter discusses a construction of a quasi-metric Souslin space with a point-countable base. A Souslin space is a linearly ordered topological space L such that L is not… Expand

Directed Homotopy in Non-Positively Curved Spaces

- Computer Science, Mathematics
- Log. Methods Comput. Sci.
- 2020

This work studies the particular case of programs using only mutexes, which are the most widely used synchronization primitive, and shows that in this case, the resulting programs have non-positive curvature. Expand

Quasi-pseudo-metrization of topological preordered spaces

- Mathematics
- 2012

Abstract We establish that every second countable completely regularly preordered space ( E , T , ⩽ ) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the… Expand

A double completion for an arbitrary T0-quasi-metric space

- Mathematics, Computer Science
- J. Log. Algebraic Methods Program.
- 2008

The question which uniformly continuous maps between T 0 -quasi-metric spaces can be extended to the constructed completions leads the author to introduce and investigate a new class of maps, which they call balanced maps. Expand

Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points

- Mathematics
- 2013

In quasi-pseudometric spaces (X,p) (not necessarily Hausdorff), the concepts of the left quasi-closed maps (generalizing continuous maps) and generalized quasi-pseudodistances J:X×X→[0,∞)… Expand

Cauchy sequences in quasi-pseudo-metric spaces

- Mathematics
- 1982

This paper considers the problem of defining Cauchy sequence and completeness in quasi-pseudo-metric spaces. The definitions proposed allow versions of such classical theorems as the Baire Category… Expand

FAMILIES OF QUASI-PSEUDO-METRICS GENERATED BY PROBABILISTIC QUASI-PSEUDO-METRIC SPACES

- Mathematics
- 2007

This paper contains a study of families of quasi-pseudo-metrics (the concept of a quasi-pseudo-metric was introduced by Wilson (22), Albert (1) and Kelly (9)) generated by proba- bilistic… Expand

SOME NEW TYPES OF CONTINUITY IN ASYMMETRIC METRIC SPACES

- Mathematics
- 2020

Using the notion of forward and backward arithmetic convergence in asymmetric metric space, we define arithmetic $ff$-continuity and arithmetic $fb$-continuity and prove some interesting results in… Expand