Some Aspects of Distancing

Authors

  • Dimiter Skordev Faculty of Mathematics and Informatics St. Kliment Ohridski University

DOI:

https://doi.org/10.7546/CRABS.2022.01.01

Keywords:

metric space, ε-separated, bounded, totally bounded, clique number, monotonic function, discontinuity point, left continuous, right continuous, semialgebraic, ordered field, quantifier elimination, computable, algebraic number

Abstract

For any metric space, two binary relations are considered: the one consisting of all ordered pairs of a positive real number and a natural number such that some finite subset of the space has cardinality equal to the second number and the distance between any two distinct elements of this subset is not less than the first number, and another defined similarly, but with “greater” instead of “not less”. If the space is totally bounded, then a partial function from natural numbers to positive reals and two functions in the inverse direction can be reasonably defined by using the relations in question. The study of these functions has been initiated by other authors, and it is continued in the paper.

Author Biography

Dimiter Skordev, Faculty of Mathematics and Informatics St. Kliment Ohridski University

Faculty of Mathematics and Informatics, St. Kliment Ohridski University
5, J. Bourchier Blvd
1126 Sofia, Bulgaria
e-mail: skordev@fmi.uni-sofia.bg

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Published

02-02-2022

How to Cite

[1]
D. Skordev, “Some Aspects of Distancing”, C. R. Acad. Bulg. Sci. , vol. 75, no. 1, pp. 3–10, Feb. 2022.

Issue

Section

Mathematics