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two papers

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  • claud_banks
    Announcing versions of papers I have been working on recently. The first is a somewhat corrected and slightly revised version of a fairly mature paper. (Its
    Message 1 of 1 , Mar 5, 2010
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      Announcing versions of papers I have been working on
      recently. The first is a somewhat corrected and slightly
      revised version of a fairly mature paper. (Its proofs,
      equations and sections are numbered as in last year's
      version.)

          http://euclid.colorado.edu/~wtaylor/approx.pdf

      The second is quite new, with obviously many things
      still to be learned.

          http://euclid.colorado.edu/~wtaylor/jumps.pdf

      The general subject of both papers is that of compatibility
      between a topological (in this case metrizable) space
      A  and a set \Sigma of (universally quantified) equations.
      (Here compatible means that \Sigma can be modeled by
      continuous operations on  A.) In the first case we consider
      continuous operations and measure how far they must
      deviate from satisfying \Sigma. In the second, we consider
      exact satisfaction, but measure how far the operations
      must then deviate from continuity. In either case, we
      obtain a numerical measure of how badly :(  A  and  \Sigma
      fail to be compatible.

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