cover image: On the Fundamentals of Analysis. Six Public Lectures delivered in February  1938 at the University of Calcutta

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On the Fundamentals of Analysis. Six Public Lectures delivered in February 1938 at the University of Calcutta

1938

Theodoros is said to have taken the next steps in the same direction by proving the irrationality of the square roots, of the non-squares from 3 to 17, but the discoverer of the irrationality of ,/ 2 was unknown to the posterity; his name has vanished and there was later a belief that he lost his life in a shipwreck as a punish- ment for his outrageous discovery, and that the mystery of irrational [...] The application of Hausdorff spaces may be considered as a geometrization; on the other hand the opportunity of deriving several theorems from one by a suitable 8choice of a topology in a set, or of the system of admissible sets, some times reminds on© of modern Algebra. [...] There will be no misinterpretation if we denote for the purpose of these lectures the set containing only one point, say a, by a. Hence a C A . (4) means that a is contained in the set A. The points contained in A &B form a set, the meet A n B . (5) of A and B; the points contained in A or B form a set, the join AUB . (6) of A and B. 1. 1. [...] Let p be a point of C not belonging to D. As D is closed, p is contained in an open set D such that [D] contains no point of D; then D fl C has the property D*; hence p is not a point of D*(C), and D*(C) = D. The class Li of all the properties corresponding to the setD contains there- fore the property D*, on the other hand, if in any subset A of C any pro- lepore)? [...] of the class A holds, the property D* holds also in A. The property D* is therefore the 'maximum' property of the class A ; it is the propeity which may be constructed by combining all the properties of the class A by or.
technology medicine science
Pages
59
Published in
India
SARF Document ID
sarf.100014
Segment Pages Author Actions
Foreword
i-iii F.W. Lwvi view
Introduction
1-42 unknown view
Ciutical and Historical Notes
43-55 unknown view
Index
56-56 unknown view

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