Some dual statements concerning Wiener measure and Baire category

The Bang-Bang theorem via Baire category. A Dual Approach

The paper develops a new approach to the classical bang-bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point x̄, we consider those which minimize an auxiliary linear functional φ. For all φ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.

On the Baire Category Theorem

Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...

Baire Category for Monotone Sets

We study Baire category for downward-closed subsets of 2ω , showing that it behaves better in this context than for general subsets of 2ω . We show that, in the downward-closed context, the ideal of meager sets is prime and b-complete, while the complementary filter is g-complete. We also discuss other cardinal characteristics of this ideal and this filter, and we show that analogous results fo...

The Baire Theory of Category

The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

Baire Category, Probabilistic Constructions and Convolution Squares