Alma mater česká Carolo-Ferdinandea - Alma mater Jagellonica. Vzájemné inspirace a kontakty mezi českou Karlo-Ferdinandovou univerzitou v Praze a Jegellonskou univerzitou v Krakově v letech 1882-1918.
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.