In this paper we establish some conditions for an almost $\pi $-domain to be a $\pi $-domain. Next $\pi $-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for $\pi $-rings.
Generalizing the notion of the almost free group we introduce almost Butler groups. An almost $B_2$-group $G$ of singular cardinality is a $B_2$-group. Since almost $B_2$-groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that $G$ is a $B_1$-group. Some other results characterizing $B_2$-groups within the classes of almost $B_1$-groups and almost $B_2$-groups are obtained. A theorem of stating that a group $G$ of weakly compact cardinality $\lambda $ having a $\lambda $-filtration consisting of pure $B_2$-subgroup is a $B_2$-group appears as a corollary.
We introduce a new class of functions called almost ˜gα-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost ˜gα-closed continuous surjections.
We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not quaternionic Kähler.
A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved.
We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It\^o processes with bounded coefficients and when the volatility is bounded away from zero.
We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on E corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain a state smearing theorem for these effect algebras, as well as the continuity of ⊕-operation in the order and interval topologies on them.
Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.