Having a small weight is determined by the small subspaces
Abstract: We show that for every cardinal and an arbitrary topological space X if we have whenever and then as well. M. G. Tkačenko proved this for spaces in . We also prove an analogous statement for the -weight if is regular.
-  I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021
-  M. G. Tkačenko, Chains and cardinals, Dokl. Akad. Nauk SSSR 239 (1978), no. 3, 546–549 (Russian). MR 0500798
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