everywhere continuous 
We describe a class of locally convex spaces on which there exist everywhere infinitely bdifferentiable real functions which are not everywhere continuous (and so are not everywhere HLdifferentiable).


The method produces spinors which are everywhere continuous with continuous derivates which is particularly important for the relativistic case.


They are e.g.λnalmost everywhere continuous and therefore show satisfactorystability behaviour w.r.t.


Homomorphisms of topological measure spaces had been defined in [5] to be measurepreserving and almost everywhere continuous mappings; this induces a concept of isomorphic topological measures.


Thus constrained optimization algorithms cannot assume an everywhere continuous null space basis.


As an application we obtain a characterization of setvalued functions defined on IRn admitting an approximately continuous or an approximately continuous and almost everywhere continuous selection.


LetX be a compact metric space, le μ be a nonnegative normalized Borel measure onX and letf be a measurable bounded realvalued function defined onX such thatf is μalmost everywhere continuous and different from zero.


Furthermore, these programs are construable as almost everywhere continuous functions from the unit interval {x  0 ≤ x ≤ 1} to the real numbers R.


The topology of almost everywhere continuous, approximately continuous functions


For singleinput multioutput C∞systems, we state conditions under which observability for every C∞input implies observability for every almost everywhere continuous, bounded input (for every L∞input in the controlaffine case).


In these cases, it is proved that the function y(r) and its first derivative are everywhere continuous, but eventually the derivative of some order becomes discontinuous at the points (n+1)σ/m, n=0, 1,....


Control can be either over a fixedtime interval, or it can terminate when a target set is reached, and there can be additional (almost everywhere continuous) side constraints.


Due to the smooth nature of variational interpolation, the gradient of the implicit function is everywhere continuous.

