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2011, Topology and its Applications
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem.
Canadian Mathematical Bulletin, 2019
We present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.
2018
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis.
arXiv (Cornell University), 2018
We shorten the proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1988
International Journal of Mathematics and Mathematical Sciences, 2001
A fixed point theorem of Fisher and Sessa is generalized to locally convex spaces and the new result is applied to extend a recent theorem on invariant approximation of Sahab, Khan, and Sessa.
2008
For an arbitrary group G it is possible to introduce the notion of generalized supersolvably embedded normal subgroup of G. Related with this notion and with the notion of generalized hypercenter of G, there are some results in the finite case. Asaad and Mohamed (Comm. Algebra, 2001) showed that in a finite group G the generalized supersolvably embedded normal subgroup of G coincides with the generalized hypercenter of G. Here is shown how this result can be extended to the infinite case.
Proceedings of the American Mathematical Society, 1981
A new direct proof of a theorem of Stanojević is given. Consequently it is proven that the Fomin class F p ( 1 > p ⩽ 2 ) {\mathcal {F}_p}(1 > p \leqslant 2) is a subclass of the class B V ∩ C \mathcal {B}\mathcal {V} \cap \mathcal {C} , where C \mathcal {C} is the Garrett-Stanojević class and B V \mathcal {B}\mathcal {V} is the class of null sequences of bounded variation. This also provides a new direct proof of Fomin’s theorem.
Analysis in Theory and Applications, 2018
In this paper, we obtain a result that improves the results of Govil and Nwaeze, Qazi and the classical result of Rivlin.
Journal of Functional Analysis, 1987
Bulletin of the Polish Academy of Sciences Mathematics, 2010
We give a simple geometric proof of Mohan Kumar's result about complete intersections.
Eprint Arxiv Math 0302321, 2003
In 1985 Xiao Gang proved that the bicanonical system of a complex surface S of general type with p 2 (S) > 2 is not composed of a pencil ([8]). In this note a new proof of this theorem is presented.
Branislav Martić Mirjana S. Vuković * Univerzitet u Sarajevu Prirodno-matematički fakultet Odsjek za matematiku UDK 517.98 Originalni naučni rad STOLZ-KARAMATA THEOREMS, PART I In memory of Jovan Karamata Abstract: This is a mainly expository paper with some additional refinements, new proofs and theorems, whose aim is to give a well rounded picture of the whole subject of Stolz-Karamata theorems. Our main points are the contributions of Jovan Karamata and his pupils, which have clarified the whole domain of Stolz-Karamata theorems. We state Stolz's theorem (Th. 1.1), point out the -version of the same theorem (Cor.1.3.1) and conclude with a simple functional version of Stolz's theorem, due to Karamata (Cor.1.3.1.), and Martić (Th.1.3.).Besides, we prove the basic Stolz's theorem, due to Karamata, and give basic improvements of Karamata's (Th. 2.3.) as well as . Then, we explain the notion of Abelian, Tauberian, and Mercerian theorems and give precise meaning to those three notations introducting Toeplitz's triangular matrix, and the summability method A connected with it.
2012
We generalize in this work, the identities obtained by Gessel, Chen and Sun, on the Bernoulii numbers. The tool used by Chen and sun is the extended Zeilberger algo-rittrm. Instead of this, we exploit a particular case of the Leibniz's formula. As corollary we recover a result analogous to the one found, by the last two mentioned authors above.
European Journal of Combinatorics, 2018
The study of 'structure' on subsets of abelian groups, with small 'doubling constant', has been well studied in the last fifty years, from the time Freiman initiated the subject. In [5] Deshouillers and Freiman establish a structure theorem for subsets of Z/nZ with small doubling constant. In the current article we provide an alternate proof of one of the main theorem of [5]. Also our proof leads to slight improvement of the theorems in [5].
Journal of Mathematical Sciences, 1987
In the paper one gives constructive proofs (without the use of the space of maximal ideals of the algebra H ~) of the Marshall-Chang theorem and of a theorem of T0 H. Wolff. These theorems are proved in the paper in a unique manner with the use of a lemma which connects the level lines of a positive harmonic function in a circle with the level lines of the inner function.
We show that, under mild assumptions on the effective, well quasi- ordered set X, one can compute a finite basis of an upward-closed subset U of X if and only if one can decide whether U !" z is empty for every z # b X. Here b X is the completion of X as defined in Finkel and Goubault-Larrecq, Forward Analysis for WSTS, Part I: Completions, STACS'09, pages 433-444, 2009. This generalizes a useful result proved by Valk and Jantzen in 1985, which is the case X = Nk.
Epicurean Ethics in Horace: The Psychology of Satire, 2018
This is the proof of the Introduction to my 2018 monograph. I plan to upload the revised and final version very soon!
Computing, 2001
We show that the assumptions of the well-known Kantorovich theorem imply the assumptions of Miranda's theorem, but not vice versa.
Proceedings of the American Mathematical Society, 1978
Necessary and sufficient conditions for 2ane" to be summable \A, \,|, whenever 2a" is convergent, have been obtained. The sufficiency part of this result has also been improved.
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