A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...

The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their i...

The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

The Semi Heyting Almost Distributive Lattice (SHADL) is a mathematical framework that combines the concepts of semi algebra and almost distributive lattice. This abstract highlights applications SHADL in various domains

In this paper we show that an algebra Ω(m,n) is functionally free for the Berman class Km,n of Ockham algebras, that is, for any two polynomials f and g, they are identically equal in Km,n if and only if f = g holds in Ω(m,n). This result can be applied to the well-known algebras, e.g., Boolean, de Morgan, Kleene, Stone, Bunge algebras, and so on.

A commutative residuated lattice is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It proved here that epimorphisms surjective in variety K such algebras (with or without involution), provided each finitely subdirectly irreducible B has two properties: (1) generated by e, and (2) poset prime...