Extraresolvability of balleans

Igor V. Protasov

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 167-175
  • ISSN: 0010-2628

Abstract

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A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.

How to cite

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Protasov, Igor V.. "Extraresolvability of balleans." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 167-175. <http://eudml.org/doc/250190>.

@article{Protasov2007,
abstract = {A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.},
author = {Protasov, Igor V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ball structure; ballean; resolvability; extraresolvability; ball structure; ballean; resolvability; extraresolvability},
language = {eng},
number = {1},
pages = {167-175},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extraresolvability of balleans},
url = {http://eudml.org/doc/250190},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Protasov, Igor V.
TI - Extraresolvability of balleans
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 167
EP - 175
AB - A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.
LA - eng
KW - ball structure; ballean; resolvability; extraresolvability; ball structure; ballean; resolvability; extraresolvability
UR - http://eudml.org/doc/250190
ER -

References

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  2. Ceder J.G., On maximally resolvable spaces, Fund. Math. 55 (1964), 87-93. (1964) Zbl0139.40401MR0163279
  3. Comfort W.W., Masaveau O., Zhou H., Resolvability in topology and topological groups, Ann. New York Acad. Sci. 767 (1995), 17-27. (1995) 
  4. Comfort W.W., García-Ferreira S., Resolvability: a selective survey and some new results, Topology Appl. 74 (1996), 149-167. (1996) MR1425934
  5. Dranishnikov A., Asymptotic topology, Russian Math. Survey 55 (2000), 71-116. (2000) Zbl1028.54032MR1840358
  6. Filali M., Protasov I., Spread of balleans, Appl. Gen. Topol., submitted. MR2153427
  7. García-Ferreira S., Malykhin V.I., Tomita A.H., Extraresolvable spaces, Topology Appl. 101 (2000), 257-271. (2000) MR1733807
  8. Hewitt H., A problem of set theoretic topology, Duke Math. J. 10 (1943), 309-333. (1943) Zbl0060.39407MR0008692
  9. Protasov I., Banakh T., Ball Structures and Colorings of Graphs and Groups, Math. Stud. Monogr. Ser. 11, VNTL, Lviv, 2003. Zbl1147.05033MR2392704
  10. Protasov I., Zarichnyi M., General Asymptology, Math. Stud. Monogr. Ser., VNTL, Lviv, 2006. MR2406623
  11. Protasov I.V., Resolvability of groups (in Russian), Mat. Stud. 9 (1998), 130-148. (1998) MR1687086
  12. Protasov I.V., Resolvability of ball structures, Appl. Gen. Topol. 5 (2004), 191-198. (2004) Zbl1062.54006MR2121788
  13. Protasov I.V., Cellularity and density of balleans, Appl. Gen. Topol., to appear. Zbl1152.54312MR2398520
  14. Roe J., Lectures on Coarse Geometry, University Lecture Series 31, American Mathematical Society, Providence, RI, 2003. Zbl1042.53027MR2007488

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