This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ-complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

The classical approach to the study of xed point semantics of deenite logic programs P utilises two main facts : (1) The set I J L of all interpretations of the underlying language L based on a given preinterpretation J forms a complete lattice under the partial order of set inclusion. (2) The immediate consequence map T P deened on I J L is lattice continuous. An application is then made of a ...

Abstract: In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0,1]. Some properties of GIVIFMs are studied using the definition of comparability of ...

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are then developed ...