Related papers: Noetherian type in topological products

This paper deals with the symmetry analysis of the Einstein Cartan theory which is an extension of the General Relativity and it accounts for the space-time torsion. We begin by applying Noether Theorem to the Lagrangian of the FRW type…

Let $\mathfrak{R}$ be a weakly noetherian variety of unitary associative algebras (over a field $K$ of characteristic 0), i.e., every finitely generated algebra from $\mathfrak{R}$ satisfies the ascending chain condition for two-sided…

It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered…

This text contributes to the foundations of the theory of global Berkovich spaces, that is to say Berkovich spaces over Banach rings with nice properties such as $\mathbf{Z}$, rings of integers of number fields, discrete valuation rings,…

In any diffeomorphism invariant theory of gravity, one can define a Noether charge arising from the invariance of the Lagrangian under diffeomorphisms. We have determined the Noether charge for scalar-tensor theories of gravity, in which…

In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

Choosing an encoding over binary strings for input/output to/by a Turing Machine is usually straightforward and/or inessential for discrete data (like graphs), but delicate -- heavily affecting computability and even more computational…

We prove the optimal Noether-Severi inequality that $\mathrm{vol}(X) \ge \frac{4}{3} \chi(\omega_{X})$ for all smooth and irregular $3$-folds $X$ of general type over $\mathbb{C}$. For those $3$-folds $X$ attaining the equality, we…

We establish the Noether inequality \[\textrm{Vol}(X)\geq \frac{4}{3}p_g(X)-\frac{10}{3}\] for all projective $3$-folds $X$ of general type with geometric genus $5\leq p_g(X)\leq 10$ where $\textrm{Vol}(X)$ is the canonical volume. This…

For a free filter $F$ on $\omega$, let $N_F=\omega\cup\{p_F\}$, where $p_F\not\in\omega$, be equipped with the following topology: every element of $\omega$ is isolated whereas all open neighborhoods of $p_F$ are of the form $A\cup\{p_F\}$…

For all nonsingular projective $n$-folds $V$ of general type, we prove the existence of Noether type inequalities in the following form: $$\text{vol}(V)\geq a_{n,k}h^0(\Omega_V^k)-b_{n,k}$$ where $0< k\leq n$, $a_{n,k}$ and $b_{n,k}$ are…

We introduce the notion of a good map between topological spaces: a continuous map $f:X \to Y$ is *good* if for every non-empty irreducible locally closed subset $U \subseteq X$, there exists a non-empty open subset $W \subseteq Y$ such…

In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element…

For a Noetherian scheme $X$ of finite Krull dimension, Neeman recently established two characterizations of the regularity of $X$ using strong generators and bounded $t$-structures on $\operatorname{Perf}(X)$. In this note, we obtain…

In the presence of suitable power spaces, compactness of $\mathbf{X}$ can be characterized as the singleton $\{X\}$ being open in the space $\mathcal{O}(\mathbf{X})$ of open subsets of $\mathbf{X}$. Equivalently, this means that universal…

We define and study Noetherian topologies for spaces of infinite sets, and infinite words. In each case, we also obtain S-representations, namely, computable presentations of the sobrifications of those spaces.

We investigate some Weihrauch problems between $\mathsf{ATR}_2$ and $\mathsf{C}_{\omega^\omega}$ . We show that the fixed point theorem for monotone operators on the Cantor space (a weaker version of the Knaster-Tarski theorem) is not…

Let $\mathcal M_X$ denote the ideal of meager subsets of a topological space $X$. We prove that if $X$ is a completely metrizable space without isolated points, then the smallest cardinality of a non-meager subset of $X$, denoted…