In this paper, bipolar valued multi fuzzy normal subnear-ring of a near-ring is introduced and some theorems are stated proved.

The set of Hausdorff continuous functions is the largest set of interval valued functions to which the ring structure of the set of continuous real functions can be extended. The paper deals with the automation of the algebraic operations for Hausdorff continuous functions using an ultraarithmetical approach.

We construct the classical ring of quotients of the algebra of continuous real-valued functions with countable range. Our construction is a slight modification of the construction given in [3]. We supply an example showing that the two constructions can be different.

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

We show that every henselian valued field L of residue characteristic 0 admits a proper subfield K which is dense in L. We present conditions under which this can be taken such that L|K is transcendental and K is henselian. These results are of interest for the investigation of integer parts of ordered fields. We present examples of real closed fields which are larger than the quotient fields o...

Abstract Given a ring endowed with order, we provide sufficient conditions for the order topology induced by to become (analogous results module orders are consequently derived). Finally, notions of Radon and regular measures transported scope module-valued through orders. Classical characterizations these obtained as well hereditariness regularity conditional ring-valued measures.