The coarsest topology for -approximately continuous functions
The Lusin-Menchoff property of fine topologies
Three results on the regularity of the curves that are invariant by an exact symplectic twist map
A theorem due to G. D. Birkhoff states that every essential curve which is invariant under a symplectic twist map of the annulus is the graph of a Lipschitz map. We prove: if the graph of a Lipschitz map h:T→R is invariant under a symplectic twist map, then h is a little bit more regular than simply Lipschitz (Theorem 1); we deduce that there exists a Lipschitz map h:T→R whose graph is invariant under no symplectic twist map (Corollary 2).Assuming that the dynamic of a twist map restricted to a...
Trajectories, first return limiting notions and rings of -connected and iteratively -connected functions
In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted ) contained between the families (widely described in literature) of Darboux Baire 1 functions () and connectivity functions (). The solutions to our problems are based, among other, on the suitable construction of the ring,...
Typical sets and typical continuous functions