相关论文: Almost Disjointness Principles and $Q$-Space Cardi…

We show that all the common definitions of quasiregular mappings $f\colon M\to N$ between two equiregular subRiemannian manifolds of homogeneous dimension $Q\geq 2$ are quantitatively equivalent with precise dependences of the…

It is proved that, on any Abelian group of infinite cardinality ${\bf m}$, there exist precisely $2^{2^{\bf m}}$ nonequivalent bounded Hausdorff group topologies. Under the continuum hypothesis, the number of nonequivalent compact and…

We introduce the cardinal invariant $aL^\prime(X)$ and show that $|X|\leq 2^{aL^\prime(X)\chi(X)}$ for any Hausdorff space $X$ (a corollary of Theorem 4.4. This invariant has the properties a) $aL^\prime(X)=\aleph_0$ if $X$ is H-closed, and…

We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/p\ZZ$, $\ZZ/p^2\ZZ$ and $\ZZ/p\ZZ\times \ZZ/q\ZZ$ for $p,q$ two distinct prime numbers. For the two first families we give a simple characterization of all functions…

A set theory is developed based on the approximations of sets and denoted by AS. In AS the set of all sets exists but the argument for Russell's and Cantor's paradox fail. The Axioms of Separation, Replacement and Foundation are not valid.…

The second author has recently shown ([20]) that any selectively (a) almost disjoint family must have cardinality strictly less than $2^{\alpeh_0}$, so under the Continuum Hypothesis such a family is necessarily countable. However, it is…

Based on the well-known cardinal characteristics $\mathfrak{s}$, $\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection…

We prove that, under the continuum hypothesis $\frak c=\aleph_1$, any ultraproduct II$_1$ factor $M= \prod_{\omega} M_n$ of separable finite factors $M_n$ contains more than $\frak c$ many mutually disjoint singular MASAs, in other words…

Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [\lambda]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} =…

An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa.$ We prove that if there is a model of $\ZFC$ with two supercompact cardinals, then there is a model of \ZFC where…

Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to generalize the classical continued fractions. In this paper, we propose an introductive fundamental study about MCFs in the field of the $p$--adic…

The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling, Sol\'e, (2001)). We give a…

In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…

We prove the following two results. Theorem A: Let alpha be a limit ordinal. Suppose that 2^{|alpha|}<aleph_alpha and 2^{|alpha|^+}<aleph_{|alpha|^+}, whereas aleph_alpha^{|alpha|}>aleph_{|alpha|^+}. Then for all n< omega and for all…

In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D, either C <= D or D <= C. However, in ZF this is no longer so. For a given infinite…

Let $p$ and $q$ be anisotropic quasilinear quadratic forms over a field $F$ of characteristic $2$, and let $i$ be the isotropy index of $q$ after scalar extension to the function field of the affine quadric with equation $p=0$. In this…

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

For a cardinal $\mathfrak{a}$, let $\mathrm{fin}(\mathfrak{a})$ be the cardinality of the set of all finite subsets of a set which is of cardinality $\mathfrak{a}$. It is proved without the aid of the axiom of choice that for all infinite…

Let $\mathfrak{i}$ denote the minimal cardinality of a maximal independent family and let $\mathfrak{a}_T$ denote the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of $2^{<\omega}$. Using a countable support…

We finish the proof of the conjecture of F. Bogomolov and F. Pop: Let $F_{1}$ and $F_{2}$ be fields finitely-generated and of transcendence degree $\geq 2$ over $k_{1}$ and $k_{2}$, respectively, where $k_{1}$ is either $\bar{\mathbb{Q}}$…