Perfect pre-images of cofinally complete metric spaces

Adalberto García-Máynez; Salvador Romaguera

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 335-342
  • ISSN: 0010-2628

Abstract

top
We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.

How to cite

top

García-Máynez, Adalberto, and Romaguera, Salvador. "Perfect pre-images of cofinally complete metric spaces." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 335-342. <http://eudml.org/doc/248423>.

@article{García1999,
abstract = {We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.},
author = {García-Máynez, Adalberto, Romaguera, Salvador},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cofinally Čech complete; paracompact; cofinally complete metric space; perfect mapping; cofinally Čech complete space; paracompact space; perfect mapping},
language = {eng},
number = {2},
pages = {335-342},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Perfect pre-images of cofinally complete metric spaces},
url = {http://eudml.org/doc/248423},
volume = {40},
year = {1999},
}

TY - JOUR
AU - García-Máynez, Adalberto
AU - Romaguera, Salvador
TI - Perfect pre-images of cofinally complete metric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 335
EP - 342
AB - We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.
LA - eng
KW - cofinally Čech complete; paracompact; cofinally complete metric space; perfect mapping; cofinally Čech complete space; paracompact space; perfect mapping
UR - http://eudml.org/doc/248423
ER -

References

top
  1. Burdick B.S., A note on completeness of hyperspaces, General Topology and Applications: Fifth Northeast Conference, eds: Susan Andima et al., Marcel Dekker, 1991, pp.19-24. Zbl0766.54008MR1142791
  2. Corson H.H., The determination of paracompactness by uniformities, Amer. J. Math. 80 (1958), 185-190. (1958) Zbl0080.15803MR0094780
  3. Császár Á., Strongly complete, supercomplete and ultracomplete spaces, Mathematical Structures-Computational Mathematics-Mathematical Modelling, Papers dedicated to Prof. L. Iliev's 60th Anniversary, Sofia, 1975, pp.195-202. 
  4. Engelking R., General Topology, Polish. Sci. Publ., Warsaw, 1977. Zbl0684.54001MR0500780
  5. Gruenhage G., Generalized metric spaces, in Handbook of Set-Theoretic Topology, eds: K. Kunen and J. Vaughan, North-Holland, 1984, pp.425-501. Zbl0794.54034MR0776629
  6. Howes N.R., Modern Analysis and Topology, Springer-Verlag, 1995. Zbl0853.54002MR1351251
  7. Isiwata T., Mappings and spaces, Pacific J. Math. 20 (1967), 455-480. (1967) Zbl0149.40501MR0219044
  8. Kelley J.C., General Topology, Van Nostrand, 1955. Zbl0518.54001MR0070144
  9. Künzi H.P.A., Romaguera S., Quasi-metric spaces quasi-metric hyperspaces and uniform local compactness, Rend. Ist. Mat. Univ. Trieste, to appear. MR1718967
  10. Rice M.D., A note on uniform paracompactness, Proc. Amer. Math. Soc. 62 (1977), 359-362. (1977) Zbl0353.54011MR0436085
  11. Romaguera S., On cofinally complete metric spaces, Questions Answers Gen. Topology 16 (1998), 165-170. (1998) Zbl0941.54030MR1642068

NotesEmbed ?

top

You must be logged in to post comments.