A new metrization theorem

F. G. Arenas; M. A. Sánchez-Granero

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 109-122
  • ISSN: 0392-4041

Abstract

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We give a new metrization theorem on terms of a new structure introduced by the authors in [2] and called fractal structure. As a Corollary we obtain Nagata-Smirnov’s and Uryshon’s metrization Theorems.

How to cite

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Arenas, F. G., and Sánchez-Granero, M. A.. "A new metrization theorem." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 109-122. <http://eudml.org/doc/194878>.

@article{Arenas2002,
abstract = {We give a new metrization theorem on terms of a new structure introduced by the authors in [2] and called fractal structure. As a Corollary we obtain Nagata-Smirnov’s and Uryshon’s metrization Theorems.},
author = {Arenas, F. G., Sánchez-Granero, M. A.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {(pre-)fractal structure},
language = {eng},
month = {2},
number = {1},
pages = {109-122},
publisher = {Unione Matematica Italiana},
title = {A new metrization theorem},
url = {http://eudml.org/doc/194878},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Arenas, F. G.
AU - Sánchez-Granero, M. A.
TI - A new metrization theorem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 109
EP - 122
AB - We give a new metrization theorem on terms of a new structure introduced by the authors in [2] and called fractal structure. As a Corollary we obtain Nagata-Smirnov’s and Uryshon’s metrization Theorems.
LA - eng
KW - (pre-)fractal structure
UR - http://eudml.org/doc/194878
ER -

References

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  2. ARENAS, F. G.- SÁNCHEZ-GRANERO, M. A., A characterization of non-archimedeanly quasimetrizable spaces, Rend. Istit. Mat. Univ. Trieste Suppl., 30 (1999), 21-30. Zbl0944.54019
  3. ARENAS, F. G.- SÁNCHEZ-GRANERO, M. A., A new aproach to metrization, Topology and its. Appl., to appear. Zbl0996.54043
  4. BURKE, D.- ENGELKING, R.- LUTZER, D., Hereditarily closure-preserving collections and metrizability, Proc.-Amer.-Math.-Soc., 51 (1975), 483-488. Zbl0307.54030MR370519
  5. ENGELKING, R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  6. FLETCHER, P.- LINDGREN, W. F., Quasi-Uniform Spaces, Lecture Notes Pure Appl. Math., 77, Marcel Dekker, New York, 1982. Zbl0501.54018MR660063
  7. HANAI, S.- MORITA, K., Closed mappings and metric spaces, Proc. Japan Acad., 32 (1956), 10-14. Zbl0073.17803MR87077
  8. MORITA, K., A condition for the metrizability of topological spaces and for n -dimensionality, Sci. Rep. Tokyo Kyoiku Daigaku Sec. A, 5 (1955), 33-36. Zbl0065.38101MR71754
  9. MORITA, K.- NAGATA, J., Topics in general topology, North Holland, 1989. Zbl0684.00017MR1053191
  10. STONE, A. H., Metrizability of decomposition spaces, Proc. Amer. Math. Soc., 7 (1956), 690-700. Zbl0071.16001MR87078
  11. ZHI-MIN, G., ℵ -spaces and g -metrizable spaces and CF family, Topology Appl., 82 (1998), 153-159. Zbl0888.54036MR1602447

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