In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

A large number of papers have been published that are devoted to showing that certain algebraic objects obtained by defining operations on the set of all continuous real-valued functions on a suitably restricted topological space determine the space. We mention but a few of them below. Let C(X), L(X), S(X) denote respectively the ring, lattice, multiplicative semigroup of all continuous real-va...

for some real number X, the symbol V denoting the lattice least upper bound. Any ring R is regular [10] if for each xER there is an xaER such that xx°x = x. It is evident that every regular F-ring R contains a maximal bounded sub-F-ring R, the F-ring of all xER satisfying equation (1.1). The relationship between a regular F-ring and its maximal bounded sub-F-ring is analogous to that between th...

A ring of continuous functions is a ring of the form C(X), the ring of all continuous real-valued functions on a completely regular Hausdorff space X. With each ideal / of C(X), we associate certain subalgebras of C(X), and discuss their structure spaces. We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces. Introducti...