Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Numerical meshes and covering meshes of approximate inverse systems of compacta


Author: Tadashi Watanabe
Journal: Proc. Amer. Math. Soc. 123 (1995), 959-962
MSC: Primary 54B35; Secondary 54F45
DOI: https://doi.org/10.1090/S0002-9939-1995-1254858-5
MathSciNet review: 1254858
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Mardešić and Rubin (1989) introduced approximate inverse systems of metric compacta by the conditions $ {({\text{A}}1)^ \ast } - {({\text{A}}3)^ \ast }$. Mardešić and Watanabe (1988) introduced approximate inverse systems of topological spaces by the conditions $ ({\text{A}}1) - ({\text{A}}3)$. In this note we show that any approximate inverse system of metric compacta satisfies $ ({\text{A}}1) - ({\text{A}}3)$ if and only if it satisfies $ {({\text{A}}1)^\ast} - {({\text{A}}3)^\ast}$ for some matrices (see Theorem 1).


References [Enhancements On Off] (What's this?)

  • [1] S. Mardešić and L. R. Rubin, Approximate inverse systems of compacta and covering dimension, Pacific J. Math. 138 (1989), 129-144. MR 992178 (90f:54058)
  • [2] -, Cell-like mappings and nonmetrizable compacta of finite cohomology dimension, Trans. Amer. Math. Soc. 313 (1989), 53-79. MR 962284 (90a:54095)
  • [3] S. Mardešić, L. R. Rubin, and N. Uglešić, A note on approximate systems of metric compacta, preprint.
  • [4] S. Mardešić and J. Segal, Shape theory, North-Holland, Amsterdam, 1982. MR 676973 (84b:55020)
  • [5] -, Stability of almost commutative inverse systems of compact, Topology Appl. 31 (1989), 285-299. MR 997496 (90e:54018)
  • [6] S. Mardešić and T. Watanabe, Approximate resolutions of spaces and mappings, Glas. Mat. Ser. III 24 (1988), 583-633. MR 1080085 (92b:54019)
  • [7] S. Mardešić and N. Uglešić, Approximate inverse systems which admit meshes, preprint.
  • [8] K. Nagami, Dimension theory, Academic Press, New York and London, 1970. MR 0271918 (42:6799)
  • [9] J. Segal and T. Watanabe, Cosmic approximate limits and fixed points, Trans. Amer. Math. Soc. 333 (1992), 1-61. MR 1145962 (93d:55002)
  • [10] T. Watanabe, Approximative shape. I-IV, Tsukuba J. Math. 11 (1987), 17-59; 11 (1987), 303-339; 12 (1988), 1-41; 12 (1989), 273-319. MR 899720 (88j:54013)
  • [11] -, Approximate resolutions and covering dimension, Topology Appl. 38 (1991), 147-154. MR 1094547 (92d:54016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B35, 54F45

Retrieve articles in all journals with MSC: 54B35, 54F45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1254858-5
Keywords: Inverse system, approximate inverse system
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society