Related papers: A zero-dimensional F-space that is not strongly ze…

We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples of spaces with this uniform property that do not follow from…

We introduce a new class of locally convex spaces $E$, under the name quasi-$(DF)$-spaces, containing strictly the class of $(DF)$-spaces. A locally convex space $E$ is called a quasi-$(DF)$-space if (i) $E$ admits a fundamental bounded…

We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This…

Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter…

We present a novel example of a 2-dimensional space-time naked singularity. The solution has a gravity singularity and no-horizon. This example is only a toy model and as such its motivation is mathematical. In the physical sense it is very…

We present a family of four-dimensional vacuum space-times with asymptotically velocity dominated singularities and without symmetries.

We show that there is no phi-recurrent generalized Sasakian-space-forms, when is a non-zero constant.

We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a…

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal…

Let F be an infinite field. We prove that the right zero divisors of a three-dimensional associative F-algebra A must form the union of at most finitely many linear subspaces of A. The proof is elementary and written with students as the…

For a real polynomial $f$ we present explicit zero-free angular sectors in the complex plane, symmetric with respect to the real axis, with angles depending only on the degree of $f$, and vertices expressed in terms of the coefficients of…

We review and investigate some basic properties of static, cylindrically symmetric spacetimes with non-zero cosmological constant, find non-singular sheet sources of these spacetimes and discuss their characteristics, and clarify their…

Let $X\subset A^{Z^d}$ be a $2$-dimensional subshift of finite type. We prove that any $2$-dimensional multidimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general…

For a function space $X(\OO)$ satisfying weak assumptions we prove that the generic function in $X(\OO)$ is totally unbounded, hence non-extendable. We provide several examples of such spaces; they are mainly localized versions of classical…

I discuss empty space, as it appears in the physical foundations of relativistic field theories and in the semiclassical study of isolated systems. Of particular interest is the relationship between empirical measurements of the…

In this paper, we consider non-normal numbers occurring in dynamical systems fulfilling the specification property. It has been shown that in this case the set of non-normal numbers has measure zero. In the present papers we show that a…

We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate…

In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis. This work includes the equivalent definitions of spherically complete spaces, their basic…