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1.
Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization that is inspired by the study of the models of non-Euclidean geometry. In this note we discuss the history of Barbilian spaces and the evolution of the theory. We point out that some of the current references to work done in Barbilian spaces refer to Barbilian's contribution from 1934, while his construction has been greatly extended in four works published in Romanian in 1959–1962. 相似文献
2.
M. Van De Vel 《Topology and its Applications》1983,16(1):81-105
Various relations between the dimension and the classical invariants of a topological convex structure have been obtained, leading to an equivalence between Helly's and Carathéodory's theorem, and to the closedness of the hull of compact sets in finite-dimensional convexities. It is also shown that the Radon number of an n-dimensional binary convexity is in most cases equal to the Radon number of the n-cube, and a natural condition is presented under which the invariants are equal to dimension plus one. 相似文献
3.
In this paper we give a detailed account of Boscovich's geometrical principle of continuity. We also compare his ideas with those of his forerunners and successors, in order to cast some light on his possible sources of inspiration and to underline the elements of novelty in his approach to the subject. 相似文献
4.
The mathematical work of Thomas Harriot (c. 1560–1621) is distinguished by extensive use of symbolism and other forms of visual imagery and by systematic use of combinations. This paper argues that these characteristics of his mathematical writing were already observable in the mid-1580s, in the phonetic alphabet he devised to record the speech of American Indians. The paper presents several little-known examples of Harriot's mathematics, demonstrating his use of symbolism both as a means of expression and as an analytic tool, and assesses Harriot's work in relation to the broader 17th-century trend toward symbolization in mathematics. 相似文献
5.
James E. Baumgartner 《Topology and its Applications》1985,19(3):211-225
Using side-by-side Sacks forcing, it is proved relatively consistent that the continuum is large and Martin's Axiom fails totally, that is, every c.c.c. space is the union of ?1 nowhere dense sets (equivelently, if P is a nontrivial partial ordering with the countable chain condition, then there are ?1 dense sets in P such that no filter in P meets them all). 相似文献
6.
The little-known Scottish mathematician William Spence was an able analyst, one of the first in Britain to be conversant with recent continental advances, and having original views. His major work on “logarithmic transcendents” gives the first detailed account of polylogarithms and related functions. A theory of algebraic equations was published just after his early death; and further essays, edited by John Herschel, were published posthumously. The most substantial of these concern an extension of his work on “logarithmic transcendents”, and the general solution of linear differential and difference equations. But awareness of Spence?s works was long delayed by their supposed unavailability. Spence?s life, the story of his “lost” publications, and a summary of all his essays are here described. 相似文献
7.
Giuseppe Di Maio Enrico Meccariello Somashekhar A. Naimpally 《Mediterranean Journal of Mathematics》2006,3(2):189-204
In this paper we use Bartle’s technique to study duality between a topological space and a function space. Normally such a
duality forms an essential part of Functional Analysis. We introduce several new topologies such as the topology of even convergence Te, the closed-cocompact topology Tk ′, the (strong) local proximal convergence.
We explore the topological groups of self-homeomorphisms of a topological space and shed light on the earlier work of Arens,
Dieudonné, Di Concilio. We also study the concepts such as evenly equidistant, functionally equicontinuous, due to Bouziad-Troallic
and topologically equicontinuous due to Royden.
In memory of Professor Enrico Meccariello who made a considerable contribution to this work and who suddenly passed away before
his time 相似文献
8.
Francesco Gana 《Historia Mathematica》1985,12(3):203-218
Starting from Peirce's repeated claims of priority with respect to Dedekind's definition of finite set [R. Dedekin, Was sind und was sollen die Zahlen? (Braunschweig: Vieweg, 1888), Definizione 64], this paper traces the history of Peirce's definition and its role in his research on the foundations of arithmetic. This brings to light some remarkable and neglected achievements of Peirce in this field. It also shows that his priority claims are unjustified, although understandable in terms of his desire for acknowledgment of his pioneering work on the foundations of arithmetic. 相似文献
9.
10.
We give some background and biographical commentary on the posthumous article [4] that appears in this journal issue by Robert Riley on his part of the early history of hyperbolic structures on some compact 3-manifolds. A complete list of Riley’s publications appears at the end of this article. 相似文献
11.
Marco Panza 《Historia Mathematica》2011,38(1):42-95
A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in which sense his geometry can be conceived as a conservative extension of EPG. I conclude by briefly discussing some structural similarities and differences between Descartes’s geometry and EPG. 相似文献
12.
John Wallis, Savilian professor of geometry at Oxford from 1649 to 1703, engaged in a number of disputes with French mathematicians: with Fermat (in 1657–1658), with Pascal (in 1658–1659), with Dulaurens (in 1667–1668), and against Descartes (in the early 1670s). This paper examines not only the mathematical content of the arguments but also Wallis’s various strategies of response. Wallis’s opinion of French mathematicians became increasingly bitter, but at the same time he was able to use the confrontations to promote his own reputation. 相似文献
13.
《Quaestiones Mathematicae》2013,36(1-3):307-319
Motivated by his previous work on proximally fine and on equi-p-fine uniform spaces, the author extends some results about equi-uniformly continuous families of functions to the general setting of equi-morphic families in a category. 相似文献
14.
Snellius’s Fundamenta Arithmetica et Geometrica (1615) is much more than a Latin translation of Ludolph van Ceulen’s Arithmetische en Geometrische Fondamenten. Willebrord Snellius both adapted and commented on the Dutch original in his Fundamenta, and thus his Latin version can be read as a dialogue between representatives of two different approaches to mathematics in the early modern period: Snellius’s humanist approach and Van Ceulen’s practitioner’s approach. This article considers the relationship between the Dutch and Latin versions of the text and, in particular, puts some of their statements on the use of numbers in geometry under the microscope. In addition, Snellius’s use of the Fundamenta as an instrument to further his career is explained. 相似文献
15.
In this paper, I examine Euler's early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Euler's first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Euler's work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation. 相似文献
16.
The mathematician John von Neumann was born in Hungary but principally received his scientific education and socialization in the German science system. He received his Habilitation from the Friedrich-Wilhelms–Universität in Berlin in 1927, where he lectured as a Privatdozent until his emigration to the USA. This article aims at making a contribution to this early part of Neumann’s scientific biography by analyzing in detail the procedure that led to his Habilitation as well as the beginnings of Neumann’s research on functional analysis. An analysis of the relevant sources shows that in Berlin in the year 1927 Neumann was not yet regarded as the outstanding mathematical genius of the 20th century. Furthermore it will be seen that Neumann had great difficulties in developing the fundamental concepts for his path breaking work in spectral theory and only managed to do so with the support of the Berlin mathematician Erhard Schmidt. 相似文献
17.
Dénes König (1884–1944) is a Hungarian mathematician well known for his treatise on graph theory (König, 1936). When he was a student, he published two books on mathematical recreations ( and ). Does his work on mathematical recreations have any relation to his work on graph theory? If yes, how are they connected? To answer these questions, we will examine his books of 1902, 1905 and 1936, and compare them with each other. We will see that the books of 1905 and 1936 include many common topics, and that the treatment of these topics is different between 1905 and 1936. 相似文献
18.
The goal of this paper is to provide an extensive account of Robert Leslie Ellis?s largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his ‘idealist’ renovation of the Baconian theory of induction and a ‘realism’ vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed to Ellis?s reformulation of the metaphysical foundations of traditional probability theory. This parallel is assessed with reference to the disagreement between Ellis and Whewell on the nature of (pure) mathematics and its relation to scientific knowledge. 相似文献
19.
Luigi Borzacchini 《Mediterranean Journal of Mathematics》2006,3(3-4):433-448
The method of exhaustion is one of the greatest achievements of Greek mathematics, but the history of its development is not
clear. First and foremost Archimedes’ role has been keenly debated, by and large undermined, so that even his name seems condemned
to disappear in the name of the Eudoxus-Archimedes Lemma. In this paper we try to revaluate his role by a new interpretation
(or, more precisely, by the refinement of an old one) of the historical development of the theory, underlining the theoretical
relevance of the problem of addition/subtraction and comparison between curves.
Dedicated to the memory of Professor Aldo Cossu 相似文献
20.
In this article, a discussion and analysis is presented of the Kujang sulhae by Nam Pyoˇng-Gil (1820-1869), a 19th-century Korean commentary on the Jiuzhang suanshu. Nam copied the problems and procedures from the ancient Chinese classic, but replaced Liu Hui’s and Li Chunfeng’s commentaries with his own. In his postface Nam expressed his dissatisfaction with the earlier commentaries, because the approaches of Liu and Li did not match those of his contemporary readers well. This can be seen from the most important features of Nam’s commentary: the use of a synthesis of European and Chinese mathematical methods, easy explanations appealing to intuition, and disuse of the methods of infinitesimals and limits in Liu’s and Li’s commentaries. Based on his own postface and these features of his commentary, I believe that Nam Pyoˇng-Gil treated the Jiuzhang suanshu as a very important historical document, which he intended to explain according to the new mathematical canon in both Qing China and Chosoˇn Korea, the Shuli jingyun. Thus the Kujang sulhae is an example of the endeavor of 19th-century Korean mathematicians to reinterpret ancient Chinese mathematical texts with their contemporary knowledge. 相似文献