The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-v...

We thank the reviewer for the valuable comments. A clarification will be made that the same set up applies for laboratory instruments. Indeed the semi-continuous (SC) instrument is not identical to the lab instrument but it does measure ECOC with the same thermal/optical method. The SC instruments participated in this comparison did n0t show any systematic deviating behavior or overall poor per...

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].

Session 1. 8:40 10:15 AM. Melamed Benjamin Rutgers University, Chair Berge’s Maximum Theorem for Non-compact Image Sets and Its Applications. Pavlo Kasyanov, Kyiv Polytechnic Institute & World Data Center, Ukraine and Eugene A. Feinberg, Stony Brook University. For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined ...

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

In some past works by the author and collaborators, the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed. Generally, the ageing function turns out to be a semi-copula. Here we focus attention on the special class of survival models whose ageing function is actually a copula. For pairs of models in this class we define a notion...

K e y w o r d s T o p o l o g y , C-scattered and scattered topological spaces. ('ompactness, Fuzzy perfect maps, S-paracompactness, S*-paracompactness. Fuzzy paracompactness. *-Fuzzy paracompactness. 1. I N T R O D U C T I O N The concept of C-sca t te red topological space has been defined by Telg{,rsky [1]. A space X is said to be C-sca t te red if each of its nonempty closed subspaces conta...