Which topologies can have immediate successors in the lattice of T1-topologies?
Submitted: 2013-11-28
|Accepted: 2013-11-28
|Downloads
Keywords:
Lattice of T1-topologies, Maximal point, KC-space, Cover of a topology, Upper topology, Lower topology
Supporting agencies:
Consejo Nacional de Ciencia y Tecnología (México)
grant 38164-E and Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo (Brasil)
Abstract:
References:
O. T. Alas, V. V. Tkachuk and R. G. Wilson, Closures of discrete sets often reflect global properties, Topology Proceedings 25 (2000), 27-44.
A. Bella, Few remarks on spaces which are generated by discrete sets, to appear.
A. Bella and V. I. Malykhin, F-points in countably compact spaces, Applied General Topology 2 no. 1 (2001), 33-37.
E. van Douwen, Applications of maximal topologies, Topology and Its Applications 51 (1993), 125-139. http://dx.doi.org/10.1016/0166-8641(93)90145-4
A. Dow, M. G. Tkachenko, V. V. Tkachuk and R. G. Wilson, Topologies generated by discrete subspaces, Glasnik Mat. Ser. III, 37 (57) no. 1 (2002), 187-210.
R. Engelking, General Topology, (Heldermann Verlag, Berlin, 1989).
L. Gillman and M. Jerison, Rings of Continuous Functions, (Van Nostrand, Princeton, NJ, 1960). http://dx.doi.org/10.1007/978-1-4615-7819-2
I. Juhász, Cardinal Functions in Topology - Ten Years Later, Mathematical Centre Tracts 123, (Amsterdam, 1980).
R. E. Larson and S. Andima, The lattice of topologies; A survey, Rocky Mountain J. of Math. 5 no. 2 (1975), 177-198. http://dx.doi.org/10.1216/RMJ-1975-5-2-177
R. E. Larson and W. J. Thron, Covering relations in the lattice of T1-topologies, Transactions of the American Mathematical Society 168 (1972), 101-111.
L. A. Steen and J. A. Seebach, Counterexamples in Topology, (Springer Verlag, New York, 1978). http://dx.doi.org/10.1007/978-1-4612-6290-9
A. K. Steiner, Complementation in the lattice of T1-topologies, Proceedings of the American Mathematical Society 17 (1966), 884-885.
E. F. Steiner and A. K. Steiner, Topologies with T1-complements, Fundamenta Mathematicae 61 (1967), 23-28.
R. M. Stephenson, Initially -compact and related spaces, in Handbook of Set-theoretic Topology, K. Kunen and J. E. Vaughan, (eds.), (North Holland, Amsterdam, 1984).
M. G. Tkachenko, V. V. Tkachuk, R. G. Wilson and I. V. Yaschenko, No submaximal topology on a countable set is T1-complementary, Proceedings of the American Mathematical Society 128 no. 1 (1999), 287-297. http://dx.doi.org/10.1090/S0002-9939-99-04984-9
R. Valent and R. E. Larson, Basic intervals in the lattice of topologies, Duke Math. J. 39 (1972), 401-411. http://dx.doi.org/10.1215/S0012-7094-72-03948-8
R. C. Walker, The Stone-Cech Compactification, (Springer-Verlag, New York, 1974).
S. Willard, General Topology, (Addison Wesley, Reading, Mass., 1970).



