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Stable maps into the Hilbert cube


Authors: Dennis J. Garity and Dale M. Rohm
Journal: Proc. Amer. Math. Soc. 104 (1988), 632-634
MSC: Primary 57N20; Secondary 54F45, 54H25, 55M10
DOI: https://doi.org/10.1090/S0002-9939-1988-0962840-4
MathSciNet review: 962840
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Abstract | References | Similar Articles | Additional Information

Abstract: A map into the Hilbert cube is stable if each composition with projection onto a finite number of factors is stable. We prove that a map from a compact metric space into the Hilbert cube is stable if and only if it is universal. As a consequence, the composition of a stable map with any self homeomorphism of the Hilbert cube is also stable.


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  • [B] P. L. Bowers, Detecting cohomologically stable mappings, Proc. Amer. Math. Soc. 86 (1982), 679-684. MR 674105 (84h:54032)
  • [GT] J. Grispolakis and E. D. Tymchatyn, On confluent mappings and essential mappings--a survey, Rocky Mountain J. Math. 11 (1981), 131-153. MR 612135 (82k:54055)
  • [H1] W. Holsztyński, Une généralisation du théorème de Brouwer sur les points invariants, Bull. Acad. Polon. Sci. Sér Sci. Math. Astronom. Phys. 12 (1964), 603-606. MR 0174041 (30:4248)
  • [H2] -, Universal mappings and fixed point theorems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astrom. Phys. 15 (1967), 433-438. MR 0221493 (36:4545)
  • [H3] -, A remark on the universal mappings of $ 1$-dimensional continua, Bull. Acad. Polon. Sci. Sér Sci. Math. Astrom. Phys. 15 (1967), 547-549. MR 0222850 (36:5900)
  • [H4] -, Universality of mappings onto the products of snake-like spaces. Relation with dimension, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 161-167. MR 0230294 (37:5857)
  • [H5] -, Universality of the product mappings onto the product of $ {I^n}$ and snake-like spaces, Fund. Math. 64 (1969), 147-155. MR 0244936 (39:6249)
  • [H6] -, On the composition and products of universal mappings, Fund. Math. 64 (1969), 181-188. MR 0243491 (39:4812)
  • [H7] -, On the product and composition of universal mappings of manifolds into cubes, Proc. Amer. Math. Soc. 58 (1976), 311-314. MR 0407832 (53:11602)
  • [HW] W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N.J., 1941. MR 0006493 (3:312b)
  • [K] J. Krasinkiewicz, Essential mappings onto products of manifolds, preprint. MR 925878 (89e:54071)
  • [N] S. B. Nadler, Universal mappings and weakly confluent mappings, Fund. Math. 110 (1980), 221-235. MR 602888 (82h:54057)
  • [W] J. J. Walsh, A class of spaces with infinite-cohomological dimension, Michigan Math. J. 27 (1980), 215-222. MR 568642 (82j:55001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0962840-4
Keywords: Stable map, essential map, universal map, essential family, strongly infinite dimensional
Article copyright: © Copyright 1988 American Mathematical Society

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