Mizar formalization of pp. 105–108 of [10] which continues [27]. We found a simplification for the proof of Corollary 1.15, in the last case, see the proof in the Mizar article for details. One can prove the following propositions: (1) Let X be a set and F be a finite family of subsets of X. Then there exists a finite family G of subsets of X such that G ⊆ F and G = F and for every subset g of ...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

An element of an effectively given domain is computable iff its basic Scott open neighbourhoods are recursively enumerable. We thus refer to computable elements as Scott computable and define an element to be Lawson computable if its basic Lawson open neighbourhoods are recursively enumerable. Since the Lawson topology is finer than the Scott topology, a stronger notion of computability is obta...

Mathematics of Domains A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Michael A. Bukatin Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions repre...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...