Volume 34, No. 2 (2024)

THE CLASS OF FUZZY GENERALIZED CLOSED SETS OF TYPE s^θ AND ITS APPLICATIONS

ANJANA BHATTACHARYYA

In this paper, a new type of generalized version of the notion of fuzzy closed set, viz., fs^θg-closed set, is introduced and studied. Using this concept as a basic tool, here we introduce and study fs^θg -open and fs^θg -closed functions, the class of which are strictly larger than that of fuzzy open and fuzzy closed functions respectively. Afterwards, we introduce and study fs^θg -continuous and fs^θg -irresolute functions. Next, we introduce fs^θg -regular, fs^θg -normal, fs^θg -compact and fs^θg -T₂-spaces and the applications of the functions defined in this paper on these spaces are discussed here.

APPLICATIONS OF ZORN'S LEMMA TO PRIMALS AND GRILLS

SHYAMAPADA MODAK(1), MONOJ KUMAR DAS(2) and CHHAPIKUL MIAH(3)

We investigate various connections between the notions of filter, ideal, grill and primal in topological spaces, then we characterize Hausdorff spaces, compact spaces and continuity of functions via limit points and cluster points of grills and primals. As a conclusion on our study on maximal primals, we provide a new proof of Tychonoff theorem.

ON FILTERS AND POSITIVE IMPLICATIVE FILTERS IN PSEUDO-BI-ALGEBRAS

DANIEL A. ROMANO

The concept of (left distributive) pseudo-BI-algebras was introduced in 2023 by A. Radfar and A. Rezaei. In this paper, in addition to proving several, previously unregistered, properties of filters in (left distributive) pseudo-BI-algebras, we introduce and discuss the concept of positive implicative filters in these algebras.

HULL-KERNEL TOPOLOGY ON A SPECIFIC CLASS OF TOPOLOGICAL ALGEBRAS

MAJID SABET(1) AND SOLMAZ NOURI(2)

Let A be a Fundamental Strongly Sequential algebra (FSS). It is known that the carrier space Φ_A is compact and Hausdorff, In this paper we introduce a topology on Φ_A, called Hull-kernel topology, which coincides with the A-topology in certain circumstances.

BOUNDEDNESS AND CONVERGENCE IN METRONLIKE STRUCTURES

RAVINDRA KUMAR SONWANE(1), RAM PRASAD(2) and SAMAJH SINGH THAKUR(3)

Based on angle properties, Sonwane and Prasad [19] established a mathematical structure called metron as a generalization of metric space. Recently Sonwane, Prasad and Thakur [20] studied metronlike structures by weakening some properties of Metron. In the present paper we investigate, in the setting of metronlike structures, properties analogous to the boundedness of sets and counterparts to the convergence and Cauchy property of a sequence.