Some Aspects of Distancing
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
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.
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Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
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