Stone-Čech remainders which make continuous images normal

Cut Points in Čech-stone Remainders

We investigate cut points of subcontinua of βR \ R. We find, under CH, the topologically smallest type of subset of R that can support such a cut point. On the other hand we answer Question 66 of Hart and van Mill’s Open problems on βω [Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 97–125] by showing that it is consistent that all cut points a...

Rigidity of Continuous Quotients

We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand–Naimark duality we conclude that the assertion “Stone–Čech remainder of the half-line has only trivial au...

'Stone walls do not a prison make'.

Algebra in the Stone - Čech Compactification and its Applications to Ramsey Theory

Let me begin by expressing my sincere gratitude to the Japanese Association of Mathematical Sciences for inviting me to present this lecture and for giving me the JAMS International Prize for 2003 . I am deeply honored. This lecture is not a survey, but simply a discussion of some topics that I find interesting. For the most recent surveys of this subject area in which I have participated see [...

Nonhomogeneity of Remainders, Ii

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...