An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes

Izvestiya Mathematics

Volumn 63, Issue 6, 1999, Pages 1263-1273

  Shkarin, S A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746726475     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM1999v063n06ABEH000271     Document Type: Article

References (12)

1. M. I. Kadets, "A proof of the topological equivalence of all separable infinite-dimensional Banach spaces", Funktsional. Anal. i Prilozhen. 1:1 (1967), 61-70;
2. English transl, in, Functional Anal. Appl. 1 (1967).
3. W. T. Gowers and B. Maurey, "The unconditional basis sequence problem", J. Amer. Math. Soc. 1993, no. 4, 851-874.
4. R. Engelking, General topology, Polish Scientific Publishers, Warsaw 1983; Russian transl., Mir, Moscow 1986.
5. J. C. Oxtoby, Measure and category, Springer, New York 1971; Russian transl., Mir, Moscow 1976.
6. P. S. Aleksandrov and B. A. Pasynkov, Introduction to dimension theory, Nauka, Moscow 1975. (Russian)
7. A. Robertson and W. Robertson, Topological vector spaces, Cambridge Univ. Press, Cambridge 1964; Russian transl., Mir, Moscow 1967.
8. R. Pol, "An infinite dimensional pre-Hilbert space non-homeomorphic to its own square", Proc. Amer. Math. Soc. 90:3 (1984), 450-454.
9. J. Van-Mill, "An infinite dimensional pre-Hilbert space all bounded linear operators on which are simple", Colloq. Math. 54:1 (1987), 29-37.
10. K. Kuratowski, Topology, vol. I, rev. aug. ed., Academic Press, New York-London 1966; Russian transl., Mir, Moscow 1966.
11. W. Marciszewski, "An infinite dimensional pre-Hilbert space without a continuous map on its own square", Bull. Acad. Polon. Sci. Ser. Math. 31:9 (1983), 393-396.
12. H. Schaefer, Topological vector spaces, Macmillan, New York-London 1966; Russian transl., Mir, Moscow 1971.