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...

in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

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.

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 we overview basic known results about the varieties generated by De Morgan triples and about the problem to find equations defining the variety generated by a concrete De Morgan triple. We also provide some alternative proofs and some new results, specially for the case of Łukasiewicz De Morgan triples.

Let us consider the algebra H-B-M , where is a distributive lattice, is a H-algebra (Heyting algebra), is a B-algebra (Brouwer algebra), < A, 0, 1,∨,∧,⇒, −̇ > is HB-algebra (semi-Boolean algebra) [10], is a de Morgan algebra, < A, 0, 1,∨,∧,⇒,∼> is a symmetrical Heyting algebra [5] and, respectively is a symmetr...