Search results for "Peano"

The Foundations of Projective Geometry in Italy from De Paolis to Pieri

2002

In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the publication of Hilbert's Grundlagen. We are particularly interested in the interrelations between the Italian and the German schools (mainly the influence of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century.

Two Paths to Logical Consequence: Pieri and the Peano School

2021

This chapter1 has two main goals. First, it will explore the “negative” avenue leading from the concepts of independence and consistency to that of logical consequence.

Six lettres de Giuseppe Peano à Robert de Montessus de Ballore

2012

Nous transcrivons et analysons six lettres inédites que Giuseppe Peano a adressées au mathématicien français Robert de Montessus de Ballore entre 1896 et 1902. Nous montrons comment ces lettres témoignent de l'activité mathématique des deux scientifiques.

The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

Frege, Peano and Russell on Descriptions: a Comparison

2000

On the structure of the set of solutions of nonlinear equations

1971

Let T be a mapping from a subset of a Banach space X into a Banach space Y. The present paper investigates the nature of the set of solutions of the equation T(x) = y for a given y E Y, i.e. when T-l(y) # 0 ? What are the topological properties of T-l(y)? A prototype for an answer to these questions is given by Peano existence theorem on the connectedness of the set of solutions of an ordinary differential equation in the real case. In its general setting, this problem was first attacked by Aronszajn [l] and Stampacchia [l 11; recently, by Browder-Gupta [5], Vidossich [12] and, above all, Browder [3, Sec. 51 who gives several interesting results in an excellent treatment. Customary, the str…

L'influenza di Peano sulla matematica palermitana

2010

On continua whose hyperspace of subcontinua is σ-locally connected

1999

Abstract We provide a structural characterization of all continua X whose hyperspace C ( X ) of all subcontinua is the countable union of Peano continua. Applying this result we prove that there exists a uniformly path connected continuum X with no continuous mapping from C ( X ) onto X.