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 prove that an n-valued function that is lower semi-continuous is also upper semi-continuous and therefore continuous, that is, an n-valued map. Several conditions are shown to be equivalent to continuity for n-valued functions, in particular the continuity of a corresponding singlevalued function to a configuration space. Consequently, splitting is related to braid groups to prove a Splittin...

We define an invariant of a multi-valued logic gate by considering the number of certain threshold functions associated with the gate. We call this invariant the continuous sensitivity of the gate. We discuss a method for analysing continuous sensitivity of a multi-valued logic gate by using experimental data about the gate. In particular, we will show that this invariant provides a lower bound...

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 $$...

We show that for any two continuous real valued functions f, g on [0, 1], the problemZ 1