|
Every Cech-analytic Baire semitopological group is a topological group
Author(s):
Ahmed
Bouziad
Journal:
Proc. Amer. Math. Soc.
124
(1996),
953-959.
MSC (1991):
Primary 22A20, 54E18, 54H15, 57S25
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Among other things, we prove the assertion given in the title. This solves a problem of Pfister.
References:
- 1.
- A. V. Arhangel'skii, On a class containing all metric and locally bicompact spaces, Dokl. Akad. Nauk. SSSR 151 (1963), 751--754; Eng. Trans., Sov. Math. Dokl. 4 (1963), 1051--1055. MR 27:2959
- 2.
- A. Bouziad, The Ellis theorem and continuity in groups, Topol. Appl. 50 (1993), 73--80. MR 94i:22002
- 3.
- N. Brand, Another note on the continuity of the inverse, Arch. Math. 39 (1982), 241--245. MR 84b:22001
- 4.
- L. G. Brown, Topological complete groups, Proc. Amer. Math. Soc. 35 (1972), 593--600. MR 46:7435
- 5.
- J. P. R. Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), 455--461. MR 82h:54012
- 6.
- R. Ellis, A note on the continuity of the inverse, Proc. Amer. Math. Soc. 8 (1957), 372--373. MR 18:745d
- 7.
- R. Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119--125. MR 19:561b
- 8.
- R. Engelking, General Topology, Heldermann Verlag, Berlin (1989). MR 91c:54001
- 9.
- R. V. Fuller, Relations among continuous and various non continuous functions, Pac. J. Math. 25 (1968), 495--509.MR 37:3536
- 10.
- G. Gruenhage, Generalized metric spaces, In K. Kunen and J. E. Vaughan (eds), Handbook of Set-Theoretic Topology (Elsevier Science Publishers) (1984), 423--501. MR 86h:54038
- 11.
- G. Hansel and J. P. Troallic, Quasicontinuity and Namioka's Theorem, Topol. Appl. 46 (1992), 135--149. MR 94a:54047
- 12.
- R. W. Hansell, Descriptive Topology, In M. Hu\v{s}ek and J. van Mill (edts), Recent Progress in General Topology (Elsevier Science Publishers) (1992), 275--315. CMP 93:15
- 13.
- J. E. Jayne and C. A. Rogers, Borel selectors for upper semicontinuous set-valued maps, Acta Math. 155 (1985), 41--79. MR 87a:28011
- 14.
- S. Kempisty, Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184--197.
- 15.
- E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173--176. MR 31:1659
- 16.
- D. Montgomery, Continuity in topological groups, Bull. Amer. Math. Soc. 42 (1936), 879--882.
- 17.
- H. Pfister, Continuity of the inverse, Proc. Amer. Math. Soc. 95 (1985), 312--314. MR 87a:22004
- 18.
- E. A. Reznichenko, Continuity in complete groups, Abstract in Tenth Summer Conference on General Topology and Applications, Amsterdam 1994, p. 135.
- 19.
- A. D. Wallace, The structure of topological semigroups, Bull. Amer. Math. Soc. 61 (1955), 95--112. MR 16:796d
- 20.
- W. Zelazko, A theorem on
division algebras, Bull. Acad. Pol. Sci. 8 (1960), 373--375. MR 23:A3198
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
22A20, 54E18, 54H15, 57S25
Retrieve articles in all Journals with MSC
(1991):
22A20, 54E18, 54H15, 57S25
Additional Information:
Ahmed
Bouziad
Affiliation:
Analyse et Modèles Stochastiques, URA C.N.R.S. 1378, U.F.R. des Sciences de Rouen, 76821 Mont Saint Aignan cedex, France
Email:
ahmed.bouziad@univ-rouen.fr
DOI:
10.1090/S0002-9939-96-03384-9
PII:
S 0002-9939(96)03384-9
Keywords:
Semitopological group,
topological group,
generalized continuity,
fragmentability
Received by editor(s):
January 19, 1994
Communicated by:
Franklin D. Tall
Copyright of article:
Copyright
1996,
American Mathematical Society
|