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2 results

  • Covering Games and the Banach-Mazur Game: K-tactics

  • Tomek Bartoszynski, Winfried Just, Marion Scheepers
  • Journal:
    Canadian Journal of Mathematics / Volume 45 / Issue 5 / 01 October 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 897-929
    Print publication:
    01 October 1993
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  • Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J, and player TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazurgame.

  • On Convex Functions Having Points of Gateaux Differentiability Which are Not Points of Fréchet Differentiability

  • J. M. Borwein, M. Fabian
  • Journal:
    Canadian Journal of Mathematics / Volume 45 / Issue 6 / 01 December 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 1121-1134
    Print publication:
    01 December 1993
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  • We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing ł1. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein.