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.

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 paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain , has been introduced and several results, similar to well-known results constrained in terms approximants, have established. Further, some clue construction using concept fractal interpolation added. last part, multi-valued operators associated with $$...

<p>For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on C ∗ (X, its subring bounded functions, and Σ(X, denote collection all rings that lie between C). We show there is natural correlation absolutely convex ideals/ prime ideals/maximal ideals/z-ideals/z ◦ -ideals in P(X, their real-valued counterparts ∩ C(X). These corr...