P-Adic metric preserving functions and their analogues
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Robert W. Vallin
Abstract
The p-adic completion ℚp of the rational numbers induces a different absolute value |⋅|p than the typical | ⋅| we have on the real numbers. In this paper we compare and contrast functions f : ℝ+ → ℝ+, for which the composition with the p-adic metric dp generated by |⋅|p is still a metric on ℚp, with the usual metric preserving functions and the functions that preserve the Euclidean metric on ℝ. In particular, it is shown that f ∘ dp is still an ultrametric on ℚp if and only if there is a function g such that f ∘ dp = g ∘ dp and g ∘ d is still an ultrametric for every ultrametric d. Some general variants of the last statement are also proved.
(Communicated by David Buhagiar )
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© 2021 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
