Umberto Cerruti

The stone-čech compactification in the category of fuzzy topological spaces

Abstract In this paper we obtain a reflective subcategory C of the category FTS of fuzzy topological spaces. The associated reflection β has properties similar to those of the ‘Stone-Cech’ compactification β and, in effect, is an extension of it. We study relations between β and β in particular subcategories of FTS; β is completely determined in the case of fuzzy topological spaces topologically generated.

Full length article: Periodic representations and rational approximations of square roots

In this paper the properties of Redei rational functions are used to derive rational approximations for square roots and both Newton and Pade approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, Redei rational functions are introduced as convergents of particular periodic continued fractions and are applied for approximating square roots in the field of p-adic numbers and to study periodic representations. Using the results over the real numbers, we show how to construct periodic continued fractions and approximations of square roots which are simultaneously valid in the real and in the p-adic field.

Completion of L-fuzzy relations

It is shown that the category L of complete L-similarities on L-sets is a full reflective subcategory of R(L) (L-fuzzy graphs); L is equivalent to Lh (L)(sheaves on L). Connections with other known “fuzzy” categories are also studied.

On the operations of sequences in rings and binomial type sequences

Given a commutative ring with identity R, many different and interesting operations can be defined over the set

Groups and monoids of Pythagorean triples connected to conics

H_R

Colored compositions, Invert operator and elegant compositions with the ''black tie''

HR of sequences of elements in R. These operations can also give

“Non-Standard” Concepts in Fuzzy Topology

H_R