The ambient homeomorphy of certain function and sequence spaces

Jan J. Dijkstra; Jerzy Mogilski

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 595-611
  • ISSN: 0010-2628

Abstract

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In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space σ . The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a σ -compactum or not.

How to cite

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Dijkstra, Jan J., and Mogilski, Jerzy. "The ambient homeomorphy of certain function and sequence spaces." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 595-611. <http://eudml.org/doc/247903>.

@article{Dijkstra1996,
abstract = {In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space $\sigma $. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a $\sigma $-compactum or not.},
author = {Dijkstra, Jan J., Mogilski, Jerzy},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hilbert space; Hilbert cube; $\mathcal \{F\}_\{\sigma \delta \}$-absorber; ambient homeomorphism; function space; $p$-summable sequence; Hilbert space; Hilbert cube; -absorber; ambient homeomorphism; function space; -summable sequence},
language = {eng},
number = {3},
pages = {595-611},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The ambient homeomorphy of certain function and sequence spaces},
url = {http://eudml.org/doc/247903},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Dijkstra, Jan J.
AU - Mogilski, Jerzy
TI - The ambient homeomorphy of certain function and sequence spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 595
EP - 611
AB - In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space $\sigma $. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a $\sigma $-compactum or not.
LA - eng
KW - Hilbert space; Hilbert cube; $\mathcal {F}_{\sigma \delta }$-absorber; ambient homeomorphism; function space; $p$-summable sequence; Hilbert space; Hilbert cube; -absorber; ambient homeomorphism; function space; -summable sequence
UR - http://eudml.org/doc/247903
ER -

References

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  8. Dobrowolski T., Mogilski J., Problems on topological classification of incomplete metric spaces, 409-429 in Open Problems in Topology, J. van Mill and G.M. Reed, eds., North-Holland, Amsterdam, 1990. MR1078661
  9. Dobrowolski T., Mogilski J., Certain sequence and function spaces homeomorphic to the countable product of l f 2 , J. London Math. Soc. 45.2 (1992), 566-576. (1992) MR1180263
  10. Lutzer D., McCoy R., Category in function spaces I, Pacific J. Math. 90 (1980), 145-168. (1980) Zbl0481.54017MR0599327
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