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P.J. Nyikos has asked whether it is consistent that every hereditarily normal manifold of dimension > 1 is metrizable, and proved it is if one assumes the consistency of a supercompact cardinal, and, in addition, that the manifold is hereditarily collectionwise Hausdorff. We are able to omit these extra assumptions.
We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizab
We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of omega_1 is hereditarily paracompact.
We prove that each metrizable space (of cardinality less or equal to continuum) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scat
We suggest the possibility that the mysterious dark energy component driving the acceleration of the Universe is the leading term, in the de Sitter temperature, of the free energy density of space-time seen as a quantum gravity coherent state of the
Given a dynamical system $(X,f)$, we let $E(X,f)$ denote its Ellis semigroup and $E(X,f)^* = E(X,f) setminus {f^n : n in mathbb{N}}$. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We sh