On (\Lambda, \theta)-closed sets and sober \theta-R₀ spaces
by
Saeid Jafari
Department of Mathematics and Physics, Roskilde University, Denmark
Coauthors: M. Caldas (Universidade Federal Fluminense, Brasil), D. N. Georgiou (University of Patras, Greece), T. Noiri (Yatsushiro College of Technology, Japan)

In 1943, Fomin [3] (see also [6]) introduced the notion of \theta-continuity. The notion of \theta-open, \theta-closed and \theta-closure subsets were introduced by Velicko [5] for the purpose studing the important class of H-closed spaces in terms of arbitrary filterbases. Dickman and Porter [1], [2] and Joseph [4] continued the work of Velicko. It is the intention of this talk to present and study the notion of (\Lambda, \theta)-closedness by utilizing the notions of \theta-\Lambda-sets and \theta-closed sets. Moreover, we introduce and investigate the low separation axiom called sober \theta-R₀ by using the above notions.

References

[1] R. F. Dickman and J. R. Porter, \theta-closed subsets of Hausdorff spaces, Pacific J. Math. 59(1975), 407-415.

[2] R. F. Dickman and J. R. Porter, \theta-perfect and \theta-absolutely closed functions, Ilinois J. Math. 21 (1977), 42-60.

[3] S. Fomin, Extensions of topological spaces, Ann. Math.( 44)(1943), 471-480.

[4] J. E. Joseph, \theta-closure and \theta-subclosed graphs, Math. Chronicle 8 (1979), 99-117.

[5] N. V. Velicko, H-closed topological spaces, Mat. Sb. 70(1966), 98-112; English transl., in Amer. Math. Soc. Transl. 78(1968), 102-118.

[6] S. Iliadis and S. Fomin, The method of centred systems in the theory of topological spaces, Uspekhi Mat. Nauk. 21(1996), 47-76=Russian Math. Surveys, 21 (1966), 37-62.

Date received: May 26, 2001