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Volume 9 - August 1966

Contents

Page 5 of 6

Book Reviews: Comptes Rendus Critiques

Notes and Problems

  • A Global Existence Theorem

  • M. Eisen
  • Published online by Cambridge University Press:
    20 November 2018, pp. 519-520
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  • The Cauchy-Peano existence theorem (1) does not allow us to decide from the form of a given system of equations whether or not its solution can be continued for the infinite interval -∞ < t < ∞. Several sufficient conditions for such a continuation were given by A. Wintner in (2). The main result of his paper is the following theorem which is not proven.

  • R1-Topological Spaces1

  • M.G. Murdeshwar, S.A. Naimpally
  • Published online by Cambridge University Press:
    20 November 2018, pp. 521-523
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  • In his paper ″Indexed systems of neighborhoods for general topological spaces″ (Amer. Math. Monthly 68, (1961), 886–893), A.S. Davis defined a hierarchy of what he called regularity axioms. The R1 -axiom is independent of both T0 and T1, but is strictly weaker than T2. In this note, we propose to study the properties of the spaces satisfying the R1 -axiom. In particular, we will show that in many well-known results, the hypothesis can be weakened from T2 to R1, which is part of our motivation in studying R1 -spaces.

Other

  • Nato Summer School on ‘Contemporary Methods of Discrete Mathematics’

  • Published online by Cambridge University Press:
    01 April 2019, p. 140
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Book Reviews: Comptes Rendus Critiques

Notes and Problems

  • On Closed, Totally Bounded Sets

  • M. G. Murdeshwar
  • Published online by Cambridge University Press:
    20 November 2018, pp. 525-526
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  • C. Goffman asserts that "… in a metric space X a set S is compact if and only if it is closed and totally bounded." [1] and "… every totally bounded sequence in a metric space has convergent subsequence." [2].

    The statements (incidentally, equivalent to each other) are both wrong, as the following counter-example shows. Take the set of all reals in the open interval (0, 1) with the usual metric. This space is closed and totally bounded, but not compact.

Books Received

  • Book received

  • Published online by Cambridge University Press:
    01 April 2019, pp. 135-136
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Notes and Problems

  • Limites Projectives de Chaines de Demi-Groupes Nilpotents

  • F. P. Gagnon
  • Published online by Cambridge University Press:
    20 November 2018, pp. 527-529
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  • Dans cette note nous étudions les demi-groupes avec zero qui vérifient la condition T:

    1

    Le théorème 1 montre que ces demi-groupes sont isomorphes à la limite projective d'une chaine de demi-groupes nilpotents. Le théorème 2 donne une façon de réaliser tout demi-groupe nilpotent.

Book Reviews: Comptes Rendus Critiques

Other

  • Abstract of Thesis

  • Published online by Cambridge University Press:
    01 April 2019, p. 139
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  • News From the Departments

  • Published online by Cambridge University Press:
    01 April 2019, pp. 137-138
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Book Reviews: Comptes Rendus Critiques

Other

  • Openings in Mathematics

  • Published online by Cambridge University Press:
    01 April 2019, pp. 141-142
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Book Reviews: Comptes Rendus Critiques

Other

  • Problems for Solution

  • Published online by Cambridge University Press:
    01 April 2019, p. 115
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  • Solution

  • Published online by Cambridge University Press:
    01 April 2019, p. 116
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Book Reviews: Comptes Rendus Critiques

Page 5 of 6