The uniform continuity theorem ( UCT ) states that every pointwise continuous real-valued function on the unit interval is uniformly continuous. In constructive mathematics, strictly stronger than decidable fan DFT , but Loeb [17] has shown two principles become equivalent by encoding functions as type-one functions. However, precise relation between such and (usually described type-two objects...

This paper proposes a new mathematical model for the open pit mine planning problem, based on continuous functional analysis. The traditional models for this problem have been constructed by using discrete 0−1 decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming (MIP) problems. Instead, we use a continuous approach which allows for a refined imposition of s...

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.

Let C(L) be the ring of real-valued continuous functions on a frame L. In this paper, strongly fixed ideals and characterization of maximal ideals of C(L) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C(L), is st...

The paper gives a brief account of the spaces of interval functions defined through the concepts of H-continuity, D-continuity and S-continuity. All three continuity concepts generalize the usual concept of continuity for real (point valued) functions. The properties of the functions in these new spaces are discussed and investigated, preserving essential properties of the usual continuous real...