It is proved that every function of finite Baire index on a separable metric space K is a D-function, i.e., a difference of bounded semi-continuous functions on K. In fact it is a strong D-function, meaning it can be approximated arbitrarily closely in D-norm, by simple D-functions. It is shown that if the n derived set of K is non-empty for all finite n, there exist D-functions on K which are ...

All polynomial many-one degrees are shown to be of second Baire category in the superset topology when witness functions are allowed to run in 2 log h n time, for any h. Any improvement of this result for the complete p-m-degrees of RE, EXP or NP implies P 6 = NP.

We consider continuous descent methods for the minimization of convex functions defined on a general Banach space. In our previous work we showed that most of them (in the sense of Baire category) converged. In the present paper we show that convergent continuous descent methods are stable under small perturbations.

We show that, in any unitary (commutative or not) Baire locally pseudoconvex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.

This paper studies the notion of Lebesgue integrable computable functions (denoted L-computable where p is an integer), that naturally extends the classical model of bitcomputable functions. We introduce L-computable Baire categories. We observe that L-computability is incomparable to the recently introduced notion of graph-computable functions. We study the convergence of Fourier series for L-...

Functions in Lploc[0,∞) where 1 ≤ p ≤ ∞ can be considered as inputs to linear systems. However, hysteresis operators of Preisach type have only been defined on much smaller space of regulated (or Baire) functions. In this paper, we re-define Play operators so that they are well defined for real valued measurable functions. We show that this definition coincides with the older definition for con...

In a previous paper we gave a representation, or way of programming continuous functions on streams, whether discrete-valued functions, or functions between streams. We gave also a combinator on the representations of stream processing functions that reflects composition. Streams are topologised a la Baire, by taking for basic open neighbourhoods the set of streams that share a given finite pre...

We show that every array (x(i; j) : 1 i < j < 1) of elements in a point-wise compact subset of the Baire-1 functions on a Polish space, whose iterated pointwise limit lim i lim j x(i; j) exists, is converging Ramsey-uniformly. An array (x(i; j) i<j) in a Hausdorr space T is said to converge Ramsey-uniformly to some x in T , if every subsequence of the positive integers has a further subsequence...