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

Colloquium Mathematicae (1998)

- Volume: 78, Issue: 1, page 119-122
- ISSN: 0010-1354

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topUehara, Shigenori. "A Hilbert cube compactification of the space of retractions of the interval." Colloquium Mathematicae 78.1 (1998): 119-122. <http://eudml.org/doc/210596>.

@article{Uehara1998,

author = {Uehara, Shigenori},

journal = {Colloquium Mathematicae},

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},

language = {eng},

number = {1},

pages = {119-122},

title = {A Hilbert cube compactification of the space of retractions of the interval},

url = {http://eudml.org/doc/210596},

volume = {78},

year = {1998},

}

TY - JOUR

AU - Uehara, Shigenori

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

JO - Colloquium Mathematicae

PY - 1998

VL - 78

IS - 1

SP - 119

EP - 122

LA - eng

KW - 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

UR - http://eudml.org/doc/210596

ER -

## References

top- [An] R. D. Anderson, A characterization of apparent boundaries of the Hilbert cube, Notices Amer. Math. Soc. 16 (1969), 429, Abstract #697-G17.
- [BS] V. N. Basmanov and A. G. Savchenko, Hilbert space as the space of retractions of an interval, Math. Notes 40 (1988), 563-566. Zbl0648.46023
- [Ch] T. A. Chapman, Dense sigma-compact subsets of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 154 (1971), 399-426. Zbl0208.51903
- [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. Zbl0857.54020
- [SU1] K. Sakai and S. Uehara, A Hilbert cube compactification of the Banach space of continuous functions, Topology Appl., to appear. Zbl0926.54008
- [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. Zbl0886.57019
- [To] H. Toruńczyk, On CE-images of the Hilbert cube and characterization of Q-manifolds, Fund. Math. 106 (1980), 31-40.

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