On -algebraic closures of -compact elements
On matrix rapid filters
Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.
On metric σ-discrete spaces
By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.
On modularity in lattices of congruences on ordered sets
On M-operators of q-lattices
It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.
On multilattices with isomorphic graphs
On Multiset Ordering
Formalization of a part of [11]. Unfortunately, not all is possible to be formalized. Namely, in the paper there is a mistake in the proof of Lemma 3. It states that there exists x ∈ M1 such that M1(x) > N1(x) and (∀y ∈ N1)x ⊀ y. It should be M1(x) ⩾ N1(x). Nevertheless we do not know whether x ∈ N1 or not and cannot prove the contradiction. In the article we referred to [8], [9] and [10].
On n-normal posets
A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.
On -modular and -distributive semilattices
On order and betweenness compatibility.
On order and geodesic alignment of a connected bigraph
On posets with isomorphic interval posets
On pseudocomplemented semilattices with Stone congruence lattices
On regularity classes of binary relations
On relations
On representation of cyclically ordered sets
On semimodular lattices of generating systems
On some hypotheses concerning trees.
On Some Intercalations In Ordered Sets
On some minimal problem