On pre-R0 and Pre-R1 topological spaces
by
Saeid Jafari
Department of Mathematics and Physics, Roskilde University , Postbox 260, 4200 Roskilde, Denmark
Coauthors: Miguel Caldas Cueva (Universidade Federal Fluminese), Takashi Noiri (Yatsushiro College of Technology)

The notion of R0 topological space introduced by N. A. Shanin (9). A. S. Davis (1) rediscovered it and investigated some of its properties. Since then, several authors investigated properties of R0 topological spaces (2), (3), (4), (7). A. S. Davis (1) introduced the notion of R1 topological spaces. Murdeshewar and Naimpally (6), Dunham (4) and Dorsett (2) further investigated this notion. I. Reilly (8) investigated pairwise R0 topological spaces and M. Mrsevic (5) considered pairwise R0 and pairwise R1 bitopological spaces.

We introduced and investigated the notions of pre-R0 and pre-R1 topological spaces by involving preopen sets. This is the purpose of this talk to present some of the characterizations of pre-R0 and pre-R1 topological spaces.

(1) A. S. Davis, Indexed systems of neighbourhoods for general topological spaces, Amer. Math. Monthly 68 (1961) 886-893.
(2)C. Dorsett, R0 and R1 topological spaces, Mat. Vesnik 2(15)(30)(1978), 117-122.
(3) K. K. Dube, A note on R0-topological spaces, Mat. Vesnik 11(26)(1974), 203-208.
(4) W. Dunham, Weakly Hausdorff spaces, Kyungpook Mathematical Journal 15(1975), 41-50.
(5) M. Mrsevic, On pairwise R0 and pairwise R1 bitopological spaces, Bull.Math. Soc. Sci. Math. R. S. de Roumanie 30(78)(2) (1986), 141-148.
(6) M.G.Murdeshewar and A. S. Naimpally, R1-topological spaces, Canad. Math. . Bull. 9(1966), 521-523.
(7)A. S. Naimpally, On R0 topological spaces, Univ. Sci. Budapest Eotvos Sect. Math. 10(1967) 53-54.
(8) I. L. Reilly, On pairwise R0 topological spaces, Ann. Soc. Sci. Bruxelles 88 (1974), 293-296.
(9) A. N. Shanin, On separation in topological spaces, Doklady SSSR, 38 (1943), 110-113.

Date received: April 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-05.