Related papers: Remote Filters and Discretely Generated Spaces
We solve a long standing question due to Arhangel'skii by constructing a compact space which has a $G_\delta$ cover with no continuum-sized ($G_\delta$)-dense subcollection. We also prove that in a countably compact weakly Lindel\"of normal…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
Given an arbitrary measurable cardinal $\kappa$, a nondiscrete Hausdorff extremally disconnected topological group of cardinality $\kappa$ is constructed.
Let $A$ be a compact $d$-rectifiable set embedded in Euclidean space $\RR^p$, $d\le p$. For a given continuous distribution $\sigma(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, our earlier results provided a method for…
Assuming an abstract comparison principle called the Ultrapower Axiom, which is motivated by the comparison process of inner model theory and generalizes the statement that the Mitchell order is linear on normal ultrafilters, we…
The left multiplicative continuous compactification of a semitopological semigroup is the universal semigroup compactification. In this paper an internal construction of a semigroup compactification of a semitopological semigroup is…
The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined.…
We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact…
It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.
We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by…
We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal $\kappa \geq \omega$, there is a poset $\mathcal P_\kappa$ preserving all…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category $\mathsf{Top}$ of topological spaces and continuous functions, to study $\textit{compactly generated…
Cicho\'n's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's, Goldstern, Kellner and Shelah constructed a forcing…
We consider a class of 3d theories with a $\mathbb Z_n$ magnetic symmetry in which confinement is generated by charge $n$ clusters of monopoles. Such theories naturally arise in quantum antiferromagnets in 2+1, QCD-like theories on $\mathbb…
In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfrak{c}=\omega_2$ implies that there is a compact pseudoradial…
We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…
We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $\tau^*$ of the natural topology of the real line $\mathbb{R}$ with properties such…
We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously…
In root finding and optimization, there are many cases where there is a closed set $A$ one likes that the sequence constructed by one's favourite method will not converge to A (here, we do not assume extra properties on $A$ such as being…