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pro vyhledávání: '"Morris, Sidney A."'
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2401.13189
Autor:
Chalebgwa, Taboka, Morris, Sidney A.
For any Liouville number $\alpha$, all of the following are transcendental numbers: $\textrm{e}^\alpha$, $\log_\textrm{e}\alpha$, $\sin \alpha$, $\cos\alpha$, $\tan\alpha$, $\sinh\alpha$, $\cosh\alpha$, $\tanh\alpha$, $\arcsin\alpha$ and the inverse
Externí odkaz:
http://arxiv.org/abs/2202.11293
This article initiates the study of topological transcendental fields $\FF$ which are subfields of the topological field $\CC$ of all complex numbers such that $\FF$ consists of only rational numbers and a nonempty set of transcendental numbers. $\FF
Externí odkaz:
http://arxiv.org/abs/2202.00837
Autor:
Morris, Sidney A.
In this note we introduce the notion of a transcendental group, that is, a subgroup $G$ of the topological group $\mathbb{C}$ of all complex numbers such that every element of $G$ except $ 0$ is a transcendental number. All such topological groups ar
Externí odkaz:
http://arxiv.org/abs/2112.12450
Autor:
Morris, Sidney A.
In 1730 James Stirling, building on the work of Abraham de Moivre, published what is known as Stirling's approximation of $n!$. He gave a good formula which is asymptotic to $n!$. Since then hundreds of papers have given alternative proofs of his res
Externí odkaz:
http://arxiv.org/abs/2010.15512
Akademický článek
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The Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient space, has remained unsolved for 85 years, but has been answered in the affirmative for special cases such as reflexive Ban
Externí odkaz:
http://arxiv.org/abs/1804.02652
The famous Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space, has remained unsolved for 85 years, though it has been answered in the affirmative for reflexive Banac
Externí odkaz:
http://arxiv.org/abs/1707.09546
We define and study the free topological vector space $\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\mathbb{V}(X)$ is a $k_\omega$-space if and only if $X$ is a $k_\omega$-space. If $X$ is infinite, then $\mathbb{V}(X)$ contains a closed
Externí odkaz:
http://arxiv.org/abs/1604.04005
Autor:
Hofmann, Karl H., Morris, Sidney A.
A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a compl
Externí odkaz:
http://arxiv.org/abs/1506.06852