On extremally disconnected topological groups

We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω^∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset.     

Syntactic characterization of closure under connected limits

Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform.     

Places of algebraic function fields in arbitrary characteristic

We consider the Zariski space of all places of an algebraic function field F|K of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a K-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space.     

The Region 1 & 3 Broadcasting‐Satellite Service Plan after WRC‐03

The 1977 Broadcasting‐Satellite Service (BSS) Plan for Region 1 & 3 had been widely acknowledged to be out‐of‐date by the late 1980s. Development of digital modulation in the early 1990s provided an opportunity to update the technical provisions of the Plan to make it more economically viable. After a decade of work and three World Radiocommunication Conferences (WRCs), the revision of Region 1 & 3 BSS Plan was finally completed in 2003. The new Plan increased channel assignments from 5 to 10 analog‐equivalent channels for each country in Region 1, and from 4 to 12 channels for each country in Region 3. Yet, despite the increase in capacity, the new Plan is surprisingly similar to the original one in terms of the technical parameters. It is still based on national coverage, and the channel plan, orbital location, orbital spacing, and polarization are also the same. As a result, the new Plan is no more economically viable to implement than the old. To create economically viable BSS systems would most likely require modifications to the assignment in the Plan. Yet, modification procedures were made more difficult to apply after replanning. Less future implementation of BSS networks than would otherwise have occurred can be expected, and an inefficient usage of these frequency bands will likely result. On the other hand, less implemented systems will mean more capacity set aside for future use. This is important for countries that currently do not have satellite operations. In the end, BSS replanning reflects the eternal conflict between efficient usage and guaranteed future access. Copyright © 2005 John Wiley & Sons, Ltd.     

A direct independence proof of Buchholz's Hydra Game on finite labeled trees

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows. Received: August 23, 1994 / Revised: July 24, 1995 and May 9, 1996     

Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

显像（示）管阴极像黑洞状缺陷形成的原因及消除对策

本文通过有关理论依据和试验数据，着重阐述了在显像（示）管测试中，阴极像中心黑洞状缺陷产生的原因以及消除这种缺陷的处理方法。通过这种处理方法处理过的显像（示）管，其整体质量水平（尤其是真空度）将会得到明显的提高。     

Countably compact topological group topologies on free Abelian groups from selective ultrafilters

Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c² using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom.     

QN-spaces, wQN-spaces and covering properties

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).