On multiplicatively perfect numbers.
The influence of Jan Marik in the field of non absolute integration is described in the plane of Czech mathematics. A short historical account on the development of integration theory in the Czech region is presented in this connection together with the recent Riemann sum approach to the general Perron integral.
A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each point x we...
Si K es un compacto no vacío en Rr, damos una condición suficiente para que la inyección canónica de ε{M},b(K) en ε{M},d(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε{M1}(F)A en ε{M2}(Rr)D donde F es un subconjunto cerrado propio de Rr y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.