Related papers: Some equivalent of extremally disconnected spaces

We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of the space of natural numbers.

We study the relative position of four subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system of four subspaces in a Hilbert space whose defect is (2n+1)/3. By an exotic system, we mean…

We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

We consider four dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

We prove the existence of almost isoperimetric extremisers for two classes of probability measures defined respectively on the Grushin space and a stratified Lie group. It turns out such extremisers can be regarded as a type of anisotropic…

It is shown that the weak $L^p$ spaces $\ell^{p,\infty}, L^{p,\infty}[0,1]$, and $L^{p,\infty}[0,\infty)$ are isomorphic as Banach spaces.

We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on $\R^d$. This time we study characterizations of these subspaces by differences.

In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.

The aim of this paper is to study Iseki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Is\'{e}ki space is quasi-compact whenever the semiring is Noetherian. We characterize Is\'{e}ki…

The known extrasolar planets exhibit many interesting and surprising features--extremely short-period orbits, high-eccentricity orbits, mean-motion and secular resonances, etc.--and have dramatically expanded our appreciation of the…

In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…

This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.

We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.

We construct a weak Hilbert space that is a twisted Hilbert space.

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

We consider extremal black hole solutions to the vacuum Einstein equations in dimensions greater than five. We prove that the near-horizon geometry of any such black hole must possess an SO(2,1) symmetry in a special case where one has an…

We obtain multirelative connectivity statements about spaces of smooth embeddings, deducing these from analogous results about spaces of Poincare embeddings that were established in our previous paper.

Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(\mu)$ on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of…