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In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essenti...
Abstract: We establish a version of a statement attributed to Kazhdan by Yau. As a corollary, we obtain a more transparent form of our uniformization theorem in complex algebraic geometry.
Abstract: This work answers the question what coverings over a topological torus can be induced from a covering over a space of dimension $k$. The answer to this question is then applied in algebro-ge...
Let k be a commutative ring. We study the behaviour of coverings of k-categories through fibre products and find a criterion for a covering to be Galois or universal.
We give a construction of quandle cocycles from group cocycles,especially quandle cocycles of the dihedral quandle Rp from group cocycles of the cyclic group Z/p.
We show exponential growth of torsion numbers for links whose first nonzero Alexander polynomial has positive logarithmic Mahler measure. This extends a theorem of Silver ndWilliams to the case of a ...
There are several equivalent ways to define continuous harmonic functions H(K) on a compact set K in Rn. One may let H(K) be the unform closures of all functions in C(K) which are restrictions of harm...
In this paper we investigate the minimum number of maximal subgroups H_i for i=1 ...k of the symmetric group S_n (or the alternating group A_n) such that each element in the group S_n (respectively A...
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which ...
We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K.~Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurst...
We answer in the armative the following question raised by H. H. Corson in 1961: " Is it possible to cover every Banach space X by bounded convex sets with nonempty interior in such a way that no poi...
We show how co-chordal covers of the edges of a graph give upper bounds on the Castelnuovo-Mumford regularity of its edge ideal. The proof is by an easy application of a deep result of Kalai and Mesh...
We analyse for which n there exist in G = An, Sn two proper subgroups H,K such that G is the union of the G-conjugacy classes of H and K.
In this paper we study a notion of a -covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We ...
A stronger form of the adjunction inequality is proved for immersed real surfaces in non simply-connected Stein surfaces. The result is applied to the geometry of Stein domains and analytic continuati...

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