A study on convergence and ideal convergence classes

Let X be a non-empty set. We introduce semi-convergence classes on X in order to obtain a modification of classical Kelley's theorem. Subsequently, we do some further investigations on ideal convergence classes (see [7]). Finally, we introduce ideal semi-convergence classes C′ on X, in order to ensure the existence of a unique topology τ on X such that: a net (sd)d∈DI-semi-convergences (C′) to x∈X i.e. ((sd)d∈D,x,I)∈C′, where I is an ideal of D, if and only if (sd)d∈DI-converges to x relative to the topology τ.