Related papers: Some Notes on Standard Borel and Related Spaces
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
The fundamental ideas of the definition of solvable and semisimple Bol algebras are given and some related theorems
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
This is a brief overview of the basic techniques of Boolean valued analysis.
Alternative approaches to Lebesgue integration are considered.
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
These short notes are meant as a quick reference for the construction of SLR(1), of LR(1), and of LALR(1) parsing tables.
We give characterizations of the Borel sets potentially in some Wadge class, among the Borel sets with countable vertical sections of a product of two Polish spaces. To do this, we use some partial uniformization results.
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
These lectures provide an introduction to the basic aspects of the Standard Model, $SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y}$.
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…
This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
In this paper we use some results related to regularity, Betti numbers and reduction of generic initial ideals, showing their stability in passing from an ideal to its initial ideal if the last has some simple properties.
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…