Stone space partitions $$\{X_{p}\mid p\in P\}$$ satisfying conditions like $$\overline{X_{p}}=\bigcup _{q\leqslant p}X_{q}$$ for all $$p\in P$$ , where P is a poset or PO system (poset with distinguished subset), arise naturally in the study both of primitive Boolean algebras and $$\omega $$ -categorical structures. A key concept studying such that p-trim open set which meets precisely those $$...

A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to ...

Markov partitions work most efficiently for Anosov systems or for Axiom A systems. However, for hyperbolic dynamical systems which are either singular or whose hyperbolicity is nonuniform, the construction of a Markov partition, which in these cases is necessarily countable, is a rather delicate issue even when such a construction exists. An additional problem is the use of a countable Markov p...

In the present work we construct non-Gaussian self-similar random fields with hierarchical structure. The construction is based on non-Gaussian solutions of the main nonlinear equation of the hierarchical models theory. The existence of such solutions was proved originally by Sinai and the author * and later by another method by Collet and Eckmann. Next we establish the uniqueness of a Gibbs st...

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

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. ...