On a certain characterisation of the semigroup of positive natural numbers with multiplication


  • Edward Tutaj Jagiellonian University, Department of Mathematics and Computer Science, Kraków; Academy of Applied Sciences in Tarnow, Department of Mathematics and Natural Sciences, Tarnów


Beurling numbers, distribution of prime numbers, Cauchy translation equation, numerical semigroups, Ap´ery sets


In this paper we continue our investigation concerning the concept of a liken. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in R. The most important examples of likens are clearly the set of natural numbers N with addition and the set of positive natural numbers N* with multiplication, represented by the sequence (ln(n+1)) n=0. The set of all likens can be parameterized by the points of some infinite dimensional, complete metric space. In this space of likens we consider elements up to isomorphism and define properties of likens as such that are isomorphism invariant. The main result of this paper is a theorem characterizing the liken N* of natural numbers with multiplication in the space of all likens.


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Kadets, Mikhail Iosifovich. "A proof of the topological equivalence of all separable infinite-dimensional Banach spaces." Funkcional. Anal. i Priložen. 1 (1967): 61-70.

Rosales, José Carlos and Pedro A. García-Sánchez. Numerical semigroups. Vol. 20 of Developments in Mathematics. New York: Springer, 2009.

Tutaj, Edward. "LikeN’s – a point of view on natural numbers." Ann. Univ. Paedagog. Crac. Stud. Math. 16 (2017): 95-115.




How to Cite

Tutaj, E. (2022). On a certain characterisation of the semigroup of positive natural numbers with multiplication. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 21, 71–92. Retrieved from https://studmath.up.krakow.pl/article/view/9607