Reflecting Lindelöfness
by
Franklin D. Tall
University of Toronto
Coauthors: James E. Baumgartner (University of Toronto)

A. Hajnal and I. Juhász asked in 1978 whether every Lindelöf space includes a Lindelöf subspace of size \aleph₁, and gave an affirmative answer, assuming CH, for compact T₂ spaces. We generalize their result to T₂ k-spaces, and also obtain Lindelöf subspaces of size \aleph₁ under CH for T₃ Lindelöf spaces which either have countable tightness or countable spread or are locally separable. We also show that there is a Lindelöf T₁ space which has no Lindelöf subspace of size \aleph₁. In Kunen's model for a saturated ideal from a huge cardinal, we show that - without assuming any separation axioms - Lindelöf first countable spaces of size not exceeding \aleph₂ have Lindelöf subspaces of size \aleph₁. For T₂ spaces, Arhangel'skii's theorem renders this trivial, but slight variations of the proof work to get similar results for various ``almost Lindelöf'' properties which are not known to bound the cardinality of T₂ first countable spaces by the continuum.

Date received: February 26, 1997

Copyright © 1997 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 # caam-22.