We define the notions of weakly μ-countably compactness and nearly denoted by Wμ-CC Nμ-CC as generalizations μ-compact spaces in sense Csaśzaŕ generalized topological spaces. To obtain a more general setting, we via hereditary classes. Using μθ-open sets, μ-regular open spaces, many results characterizations have been presented. Moreover, use properties functions to investigate effects some typ...

Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, order to characterise bisimilarity, we move the setting of intuitionistic modal logics. logic introduced, called $\mathcal{OM}$, such that modalities are closed under substitutions, induces a property known as hereditary. Intuitionistic hereditary reflects lazy instantiation performed when ch...

The mean-square filtering problem for hereditary dynamic systems is considered. It is assumed that the “main” subsystem is weakly connected with other “unimportant” components. A reduced filter for the estimation of the “main” components is used. A guaranteed level of nonoptimality for the simplified reduced filter is constructed. This level can be computed without solving the full-dimensional ...

The main aim of this work is to introduce and study the notions generalized regularity, normality, symmetric in fuzzy soft topological spaces via closed sets. Investigating some their basic properties. Many related theorems relations these are presented. Moreover, hereditary property preservation discussed.

We prove that the Continuum Hypothesis is consistent with the statement that countably compact regular spaces that are hereditarily of countable π–character are either compact or contain an uncountable free sequence. As a corollary we solve a well–known open question by showing that the existence of a compact S–space of size greater than א1 does not follow from the Continuum Hypothesis.

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1, . . . ,Pn are properties of graphs, then a (P1, . . . ,Pn)-decomposition of a graph G is a partition E1, . . . , En of E(G) such that G[Ei], the subgraph of G induced by Ei, is in Pi, for i = 1, . . . , n. We define P1⊕· · ·⊕ Pn as the property {G ∈ I : G has a ...

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.