Pairwise fuzzy irresolute mappings

summary:In this paper the concepts of fuzzy irresolute and fuzzy presemiopen mappings due to Yalvac [12] are generalized to fuzzy bitopological spaces and their basic properties and characterizations are studied

LINEAR TO NON-LINEAR TOPOLOGY VIA γ-OPEN SETS IN THE ENVIRONMENT OF BITOPOLOGICAL SPACES

Generalizations of open sets always gives a linear structure in an ordinary topological space. This paper proposes that there exists a non-linear structure in a given bitopological space via $\gamma$-open sets of the context. The new structure is also studied in the light of hyperconnectedness to show that it is completely independent with the original one. Also, the relationships between extremally disconnectedness, connectedness and hyperconnectedness are presented in the same environment by means of $\gamma$-open set. Moreover, the idea of maximal $\gamma$-hyperconnectedness is initiated in this work and some important results related to filter, ultrafilter, door space are established. Finally, some functions concerned with $(1, 2) \gamma$-open sets are introduced and interrelationships among them are produced. Some suitable examples and counter examples are properly placed to make the paper self sufficient

Weakly Generalized β- Continuous Mapping in Neutrosophic Bitopological Spaces

This paper explores the notion of β-continuity in neutrosophic bitopological spaces, a specialized area of mathematics that extends classical topological concepts to handle indeterminate or uncertain information. The study begins with the introduction of τ₁τ₂ semi-closed sets and τ₁τ₂-weakly continuous functions, which are fundamental building blocks. Key results include Proposition 2.1.3, which characterizes τ₁τ₂-weakly β-continuous mappings in terms of pre-images and β-interiors of open sets in the codomain space. Propositions 2.1.4 and 2.1.5 establish equivalent conditions for τ₁τ₂-weakly β-continuous functions involving pre-images, closures, and regular closed sets. Propositions 2.1.6 and 2.1.7 provide alternative characterizations of τ₁τ₂-weakly β-continuous functions, revealing connections with β-interiors and pre-image relationships. These findings contribute to the understanding of topological properties in neutrosophic bitopological spaces, offering valuable insights for further research in this intricate field

Near ω-continuous multifunctions on bitopological spaces

In this paper, we introduce and study basic characterizations, several properties of upper (lower) nearly (i; j)-!-continuous multifunctions on bitopological space

Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics

[EN] This paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor Ed : L-Top → L-BiTop and the “cross” functor E× : L-BiTop → L2-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis lattice-valued bitopology and the fact that the class of L2-Top’s is strictly smaller than the class of L-Top’s encompassing fixed-basis topology, the class of E×’s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.Support of Youngstown State University via a sabbatical for the 2005–2006 academic year is gratefully acknowledged.Rodabaugh, S. (2008). Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics. Applied General Topology. 9(1):77-108. doi:10.4995/agt.2008.1871.SWORD771089

ON r-FUZZY λ-CLOSED SETS AND SMOOTH FUZZY λ-CONTINUOUS FUNCTIONS

This paperdeals with the interrelations of r-fuzzy -closed sets with other types of closed sets with the suitable counter examples. Also, the interrelations of smooth fuzzy -continuous functions with other types of smooth fuzzy continuous functions are established with the necessary counter examples.Finally, the properties and the characterizations of smooth fuzzy -compact spaces are discussed