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9 papers · 1 filter
First Countable Continua and Proper Forcing
Joan E. Hart, Kenneth Kunen
Assuming the Continuum Hypothesis, there is a compact first countable connected space of weight aleph_1 with no totally disconnected perfect subsets. Each such space, however, may…
Amalgams, connectifications, and homogeneous compacta
David Milovich
We construct a path-connected homogenous compactum with cellularity 2^omega that is not homeomorphic to any product of dyadic compacta and first countable compacta. We also prove s…
Characterizing Subgroups of Compact Abelian Groups
Dikran Dikranjan, Kenneth Kunen
We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (…
Limits in compact abelian groups
Joan E. Hart, Kenneth Kunen
Let X be compact abelian group and G its dual (a discrete group). If B is an infinite subset of G, let C_B be the set of all x in X such that <phi(x) : phi \in B> converges to 1. I…
Compact Scattered Spaces in Forcing Extensions
Kenneth Kunen
We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models where the continuum is aleph_2 in which no such space can…
Complex Function Algebras and Removable Spaces
Joan E. Hart, Kenneth Kunen
The compact Hausdorff space X has the Complex Stone-Weierstrass Property (CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem. W. Rudin showed that all scat…