ArticleOriginal scientific text

Title

A Hilbert cube compactification of the space of retractions of the interval

Authors 1

Affiliations

  1. Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan

Keywords

upper semi-continuous multi-valued function, the hyperspace of non-empty compact sets, the Hausdorff metric, the pseudo-interior, the Hilbert cube, The space of retractions

Bibliography

  1. [An] R. D. Anderson, A characterization of apparent boundaries of the Hilbert cube, Notices Amer. Math. Soc. 16 (1969), 429, Abstract #697-G17.
  2. [BS] V. N. Basmanov and A. G. Savchenko, Hilbert space as the space of retractions of an interval, Math. Notes 40 (1988), 563-566.
  3. [Ch] T. A. Chapman, Dense sigma-compact subsets of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 154 (1971), 399-426.
  4. [Fe] V. V. Fedorchuk, Completions of spaces of functions on compact spaces with respect to the Hausdorff uniformity, Trudy Sem. Petrovsk. 18 (1995), 213-235 (in Russian); English transl.: J. Math. Sci. 80 (1996), 2118-2129.
  5. [SU1] K. Sakai and S. Uehara, A Hilbert cube compactification of the Banach space of continuous functions, Topology Appl., to appear.
  6. [SU2] K. Sakai and S. Uehara, A Q-manifold compactification of the homeomorphism group of a graph, Bull. Polish Acad. Sci. Math. 45 (1997), 281-286.
  7. [To] H. Toruńczyk, On CE-images of the Hilbert cube and characterization of Q-manifolds, Fund. Math. 106 (1980), 31-40.
Pages:
119-122
Main language of publication
English
Received
1997-07-01
Accepted
1998-02-04
Published
1998
Exact and natural sciences