Hyperspaces of infinite-dimensional compacta

Helma Gladdines; Jan Van Mill

Compositio Mathematica (1993)

  • Volume: 88, Issue: 2, page 143-153
  • ISSN: 0010-437X

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Gladdines, Helma, and Van Mill, Jan. "Hyperspaces of infinite-dimensional compacta." Compositio Mathematica 88.2 (1993): 143-153. <http://eudml.org/doc/90242>.

@article{Gladdines1993,
author = {Gladdines, Helma, Van Mill, Jan},
journal = {Compositio Mathematica},
keywords = {space of infinite dimensional subsets; absorbing system; hyperspace; cohomological dimension; infinite product of non-degenerate Peano continua; -absorber; pseudo-boundary of the Hilbert cube; locally infinite-dimensional Peano continuum},
language = {eng},
number = {2},
pages = {143-153},
publisher = {Kluwer Academic Publishers},
title = {Hyperspaces of infinite-dimensional compacta},
url = {http://eudml.org/doc/90242},
volume = {88},
year = {1993},
}

TY - JOUR
AU - Gladdines, Helma
AU - Van Mill, Jan
TI - Hyperspaces of infinite-dimensional compacta
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 88
IS - 2
SP - 143
EP - 153
LA - eng
KW - space of infinite dimensional subsets; absorbing system; hyperspace; cohomological dimension; infinite product of non-degenerate Peano continua; -absorber; pseudo-boundary of the Hilbert cube; locally infinite-dimensional Peano continuum
UR - http://eudml.org/doc/90242
ER -

References

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  1. 1 J. Baars, H. Gladdines, and J. van Mill.Absorbing systems in infinite-dimensional manifolds. To appear in Top. Appl. Zbl0794.57005MR1217483
  2. 2 C. Bessaga and A. Pelczyński.Selected topics in infinite-dimensional topology. PWN, Warszawa, 1975. Zbl0304.57001MR478168
  3. 3 M. Bestvina and J. Mogilski.Characterizing certain incomplete infinite-dimensional absolute retracts. Michigan Math. J., 33, 291-313, 1986. Zbl0629.54011MR856522
  4. 4 R. Cauty.L'espace des functions continues d'un espace métrique dénombrable. Proc. Am. Math. Soc., 113, 493-501, 1991. Zbl0735.54008MR1075943
  5. 5 D.W. Curtis.Hyperspaces of finite subsets as boundary sets. Top. Appl., 22, 97-107, 1986. Zbl0575.54009MR831185
  6. 6 D.W. Curtis and M. Michael.Boundary sets for growth hyperspaces. Top. Appl., 25, 269-283, 1987. Zbl0627.54004MR889871
  7. 7 D.W. Curtis and R.M. Schori.Hyperspaces of Peano continua are Hilbert cubes. Fund. Math., 101, 19-38, 1978. Zbl0409.54044MR512241
  8. 8 J.J. Dijkstra and J. Mogilski.The topological product structure of systems of Lebesgue spaces. Math. Annalen, 290, 527-543, 1991. Zbl0734.46013MR1116236
  9. 9 J.J. Dijkstra, J. van Mill, and J. Mogilski.The space of infinite-dimensional compact spaces and other topological copies of (l2f)ω. Pac. J. Math., 152, 255-273, 1992. Zbl0786.54012
  10. 10 T. Dobrowolski, W. Marciszewski, and J. Mogilski.On topological classification of function spaces Cp(X) of low borel complexity. Trans. Amer. Math. Soc., 678, 307-324, 1991. Zbl0768.54016MR1065602
  11. 11 A.N. Dranišnikov.On a problem of P. S. Alexandrov. Matem. Sbornik, 135, 551-557, 1988. Zbl0643.55001
  12. 12 J. Dydak, J.J. Walsh.Dimension, cohomological dimension, and Sullivan's conjecture. Preprint. Zbl0822.55001
  13. 13 J. van Mill.Infinite-Dimensional Topology: prerequisites and introduction. North-Holland Publishing Company, Amsterdam, 1989. Zbl0663.57001MR977744
  14. 14 H. Toruńczyk.Concerning locally homotopy negligible sets and characterizations of l2manifolds. Fund. Math., 101, 93-110, 1978. Zbl0406.55003MR518344
  15. 15 J.J. Walsh.Dimension, cohomological dimension and cell-like mappings. In S. Mardešić and J. Segal, editors, Shape Theory and Geometric Topology Conference, Dubrovnik, Lecture Notes in Mathematics870, pages 105-118. Springer, Berlin, 1981. Zbl0474.55002MR643526

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