Forcing tightness in products of fans

Jörg Brendle; Tim La Berge

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 3, page 211-226
  • ISSN: 0016-2736

Abstract

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We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.

How to cite

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Brendle, Jörg, and La Berge, Tim. "Forcing tightness in products of fans." Fundamenta Mathematicae 150.3 (1996): 211-226. <http://eudml.org/doc/212172>.

@article{Brendle1996,
abstract = {We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.},
author = {Brendle, Jörg, La Berge, Tim},
journal = {Fundamenta Mathematicae},
keywords = {-fan; gaps; tightness of a point; -good set; forcing; c.c.c. partial order; -cwH space; first countable spaces},
language = {eng},
number = {3},
pages = {211-226},
title = {Forcing tightness in products of fans},
url = {http://eudml.org/doc/212172},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Brendle, Jörg
AU - La Berge, Tim
TI - Forcing tightness in products of fans
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 3
SP - 211
EP - 226
AB - We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.
LA - eng
KW - -fan; gaps; tightness of a point; -good set; forcing; c.c.c. partial order; -cwH space; first countable spaces
UR - http://eudml.org/doc/212172
ER -

References

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  1. [Br] J. Brendle, notes. 
  2. [FS] W. G. Fleissner and S. Shelah, Incompactness at singulars, Topology Appl. 31 (1989), 101-107. Zbl0659.54016
  3. [G] G. Gruenhage, k-spaces and products of closed images of metric spaces, Proc. Amer. Math. Soc. 80 (1980), 477-482. 
  4. [H] F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. Königl. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334. Zbl40.0446.02
  5. [J] H. Judah, private communication. 
  6. [K] P. Koszmider, Kurepa trees and topological non-reflection, preprint. Zbl1076.54003
  7. [Ku] K. Kunen, Inaccessibility properties of cardinals, Ph.D. dissertation, Stanford, 1968. 
  8. [LL] T. LaBerge and A. Landver, Tightness in products of fans and psuedo-fans, Topology Appl. 65 (1995), 237-255. Zbl0867.54001
  9. [R] F. Rothberger, Sur les familles indénombrables de suites de nombres naturels et les problèmes concernant la propriété C, Proc. Cambridge Philos. Soc. 37 (1941), 109-126. Zbl67.0990.01
  10. [T] S. Todorčević, My new fan, preprint. 

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