We introduce and study a topology on nominal sets induced by a support closure operator, which arises naturally from the action of finitary permutations on a countable set of atoms. This topology is generated by support classes and is closely related to a metric defined via symmetric differences of supports. We characterize continuous maps between nominal sets in this topological setting, investigate compactness and Hausdorffness properties and analyze the interplay between equivariance, support closure and topological structure. Our results provide new insights into the algebraic and topological aspects of nominal sets, enriching their theory and potential applications in areas such as logic, computer science and algebraic structures with name-binding.
Let G be a locally compact group and 1 <= p < oo. In this paper, we show that the mapping pi : G & times; L-p(G) -> L-p(G) with the assignment (t, f) bar right arrow T(t)f = phi/delta(t)*phi delta(t) * f, is separately continuous which ensures that {T-t}(t is an element of G) forms a C-0-semigroup. Also, it is proved that the C-0-semigroup {T-t}(t is an element of G) admits a universal vector only when G is noncompact and second countable. The hypercyclic phenomenon is studied for the single weighted translation as well. Finally, we give examples of universal C-0-semigroups.
Dense fuzzy sets play an inevitable role in exploring various aspects of fuzzy topological spaces. The present paper aims at investigating the properties of dense fuzzy sets in different fuzzy topological spaces. Several characterization theorems and other novel results are obtained by means of dense fuzzy sets in specific contexts as well as in general settings. The relationship between quasi-coincidence of fuzzy sets and denseness property is also analyzed. Additionally, the concepts of separability, Q-separability, beta-separability and Q-beta-separability are examined.
This research work deals with generalizations and refinements of bounds of the first inequality of the celebrated Her-mite Hadamard dual inequality via Riemann-Liouville fractional integrals. Specifically, we explore generalized integral inequalities for several kinds of convexities using fractional integrals by utilizing the newly defined class of (s1, s2, t1, t2)-convex functions. The proposed research work establishes the superiority of an enhanced version of the power-mean integral inequality and H & ouml;lder integral inequality, termed as improved power-mean and H & ouml;lder-& Idot;& scedil;can integral inequalities, over the traditional ones.
In mathematical interpretations, integral inequalities constitute a significant and continuous body of research. Recently, numerous studies have been conducted on fractional calculus approaches due to their widespread usage in science. The tempered fractional integral is a fundamental notion in fractional calculus. Our main goal in this work is to obtain some Bullen-type inequalities utilizing the tempered fractional integral operators. From a new identity, we derive several novel Bullen-type inequalities for differentiable convex functions.
