A function f is continuous iff the pre-image f[V ] of any open set V is open again. Dual to this topological property, f is called open iff the image f [U ] of any open set U is open again. Several classical Open Mapping Theorems in Analysis provide a variety of sufficient conditions for openness. By the Main Theorem of Recursive Analysis, computable real functions are necessarily continuous. I...

Nowadays ICT is the integral part of modern teacher’s and scholar’s activity. For teachers it is reasonable to allocate two basic approach of ICT use: e-learning courses designing (to satisfaction of educational needs of students and implementation of new educational approaches) and openness in the presentation of their own research interests. For effective implementation of these approaches it...

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y , where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.