A countably compact free Abelian group whose size has countable cofinality

I. Castro Pereira, A.H. Tomita
DOI: https://doi.org/10.4995/agt.2004.1998

Abstract

Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “k-Lindelöfness” and ”k-compactness” for cardinals k. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result of Som Naimpally, to who this article is hearty dedicated.


Keywords

Forcing; Countably compact group; Convergence; Continuum Hypothesis; Countable cofinality; Size

Full Text:

PDF

References

W. W. Comfort, K. H. Hofmann and D. Remus, Topological groups and semigroups, Recent progress in general topology (Prague, 1991), 57–144, North-Holland, Amsterdam, 1992.

E. K. van Douwen, The weight of a pseudocompact (homogeneous) space whose cardinality has countable cofinality, Proc. Amer. Math. Soc. 80 (1980), 678–682. http://dx.doi.org/10.1090/S0002-9939-1980-0587954-5

P. B. Koszmider, A. H. Tomita and S. Watson, Forcing countably compact group topologies on a larger free Abelian group, Topology Proc. 25 (Summer 2000), 563–574.

K. Kunen, Set theory. An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, 102. North-Holland Publishing Co., Amsterdam, 1980. xvi+313.

M. G. Tkachenko, Countably compact and pseudocompact topologies on free abelian groups, Izvestia VUZ. Matematika 34 (1990), 68–75.

A. H. Tomita, Two countably compact groups: one of sizeNω and the other of weight Nω Without non-trivial convergent sequences, to appear in Proc. Amer. Math. Soc.

Abstract Views

1159
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share

 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Countably compact topological group topologies on free Abelian groups from selective ultrafilters
Roberto E. Madariaga-Garcia, Artur Hideyuki Tomita
Topology and its Applications  vol: 154  issue: 7  first page: 1470  year: 2007  
doi: 10.1016/j.topol.2006.03.028



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt