We analyze the numerical representability of total preorders defined on semitopological real algebras through continuous order-preserving real-valued functions that are also additive and multiplicative. The results obtained are used to interpret important concepts arising in Social Choice theory.

Continuity and Logical Completeness. An application of sheaf theory and topoi. section: Category theory The notion of a continuously variable quantity can be regarded as a generalization of that of a particular (constant) quantity, and the properties of such quantities are then akin to, and derived from, the properties of constants. For example, the continuous, real-valued functions on a topolo...

In this paper, two outwardly different graphs, namely, the zero-divisor graph [Formula: see text] and comaximal of ring all real-valued continuous functions having countable range, defined on any zero-dimensional space text], are investigated. It is observed that these graphs exhibit resemblance, so far as diameters, girths, connectedness, triangulatedness or hypertriangulatedness concerned. Ho...

In this paper we aim at an analog characterization of the classical P 6= NP conjecture of Structural Complexity. We consider functions over continuous real and complex valued variables. Subclasses of functions can be defined using Laplace transforms adapted to continuous-time computation, introducing analog classes DAnalog and NAnalog. We then show that if DAnalog 6= NAnalog then P 6= NP .

If X is a Tychonoff space, C(X) its ring of real-valued continuous functions. In this paper, we study non-essential ideals in C(X). Let a be a infinite cardinal, then X is called a-Kasch (resp. ā-Kasch) space if given any ideal (resp. z-ideal) I with gen (I) < a then I is a non-essential ideal. We show that X is an א0-Kasch space if and only if X is an almost P -space and X is an א1-Kasch space...

subject to Gj(x, t) ≤ 0 for all t ∈ Tj , j ∈ q, Hk(x, s) = 0 for all s ∈ Sk, k ∈ r, x ∈ X, where q and r are positive integers, X is a nonempty open convex subset of Rn (n-dimensional Euclidean space), for each j ∈ q ≡ {1, 2, . . . , q} and k ∈ r, Tj and Sk are compact subsets of complete metric spaces, f and g are real-valued functions defined on X, for each j ∈ q, z → Gj(z, t) is a real-value...

In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.