Markov's Fourth Question
by
W. W. Comfort
Wesleyan University

The question was asked in 1945 by Markov whether every infinite group admits a non-discrete group topology. In this largely expository talk we survey some of the literature deriving from this question, with emphasis on the Abelian case (where the brief answer is ``Yes").

Sample theorem of Berarducci et al., extending earlier results: For Abelian G with |G|=\gamma >= \omega, the poset of totally bounded Hausdorff group topologies on G contains the lattice P(2^\gamma).

Finally if time permits we summarize recent joint work with Remus concerning the size and structure of a certain ``interval" [T₀, T₁] of topologies on a fixed (not necessarily Abelian) group.

Date received: March 19, 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 # caan-01.