منابع مشابه
Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies
Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This ...
متن کاملLattice Operators and Topologies
Working within a complete not necessarily atomic Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors. We consider properties of such lattices and their interrelations. Ma...
متن کاملL-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic
In the present paper we introduce and study L-pre-T0-, L-pre-T1-, L-pre-T2 (L-pre-Hausdorff)-, L-pre-T3 (L-preregularity)-, L-pre-T4 (L-pre-normality)-, L-pre-strong-T3-, L-pre-strong-T4-, L-pre-R0-, L-pre-R1-separation axioms in (2, L)-topologies where L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the ”∧” is distribut...
متن کاملFinite Intervals in the Lattice of Topologies
We discuss the question whether every finite interval in the lattice of all topologies on some set is isomorphic to an interval in the lattice of all topologies on a finite set – or, equivalently, whether the finite intervals in lattices of topologies are, up to isomorphism, exactly the duals of finite intervals in lattices of quasiorders. The answer to this question is in the affirmative at le...
متن کاملCovering Relations in the Lattice of ^-topologies
A topology ^"i is said to cover another topology T3 if ^Ç^i and no other topology may be included between the two. In this paper, we characterize the relationship between a Tj-topology and its covers. This characterization is used to prove that the lattice of 7\-topologies is both upper and lower semimodular. We also prove that the sublattice generated by the covers of a 7\-topology is isomorph...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 2012
ISSN: 0899-6180
DOI: 10.35834/mjms/1352138564