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We define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their basic properties. We also prove that the set of points…
We define separating properties for normal ultrafilters. We prove that compactness and supercompactness are separable, yet compactness and measurability are not. We describe how to use separating properties in order to elicit distinct…
It is shown that a set in product of $n$ metrizable spaces is the discontinuity points set of some separately continuous function if and only if this set can be represented as the union of a sequence of $F_{\sigma}$-sets which are locally…
Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we…
A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.
We introduce a stronger version of an $\omega_1$-guessing model, which we call an indestructibly $\omega_1$-guessing model. The principle IGMP states that there are stationarily many indestructibly $\omega_1$-guessing models. This…
It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…
It is known that if $M,\,N$ are continuous two-variable means such that $|M(x,y)-N(x,y)| < |x-y|$ for every $x,\ y$ with $x\ne y$, then there exists a unique invariant mean (which is continuous too). We are looking for invariant means for…
The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively…
It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a…
We give a (consistent) example of a first-countable continuum that is not a remainder of the real line.
Multiparameter persistence modules can be uniquely decomposed into indecomposable summands. Among these indecomposables, intervals stand out for their simplicity, making them preferable for their ease of interpretation in practical…
Entanglement is known to be a relative notion, defined with respect to the choice of physical observables to be measured (i.e., the measurement setup used). This implies that, in general, the same state can be both separable and entangled…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
For any compact, connected metric space $(M,d)$ the set of points where $M$ is not weakly locally connected is shown to define a partition $\sP$ of $M$ for which the corresponding quotient metric space $(\sQ, \nabla_\sQ)$ is a Peano…
Continuity of measure asserts that the measure of the union of an increasing sequence of sets is equal to the supremum of the measures of those sets. We provide counter examples in the case of uncountable unions. We construct the first…
We discuss on very general grounds possible lineshapes of composite particles with one unstable constituent. Expressions are derived in a coupled-channel formalism for constituents interacting in an S-wave with no assumption made on the…