TY - JOUR
AU - Tutaj, Edward
PY - 2022/11/28
Y2 - 2023/12/06
TI - On a certain characterisation of the semigroup of positive natural numbers with multiplication
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 21
IS -
SE - Published
DO -
UR - https://studmath.up.krakow.pl/article/view/9607
SP - 71-92
AB - <p>In this paper we continue our investigation concerning the concept of a <em> liken</em>. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in <strong>R</strong>. The most important examples of likens are clearly the set of natural numbers <strong>N</strong> with addition and the set of positive natural numbers <strong>N<sup>*</sup></strong> with multiplication, represented by the sequence (ln(<em>n+1</em>))<sup>∞</sup> <sub><em>n=0</em></sub>. The set of all likens can be parameterized by the points of some infinite dimensional, complete metric space. In this <em> space of likens</em> we consider elements up to isomorphism and define <em>properties of likens</em> as such that are isomorphism invariant. The main result of this paper is a theorem characterizing the liken <strong>N<sup>*</sup></strong> of natural numbers with multiplication in the space of all likens.</p>
ER -