On the ℑ-R0 spaces and ℑ-strong quasi-uniform convergence

Using ideals, we introduce a new class of topological spaces that are more general concept than R0 spaces [Cs´asz´ar, ´ A.: General Topology. Akad- ´emiai Kiad´o, Budapest, 1978]. Different properties will be studied for that class of topological spaces. We also define a new kind of convergence for sequences of functions and formulate more general results to those contained in [Sochaczewska, A.: The strong quasi-uniform convergence, Math. Montisnigri 15 (2002), 45-55].