Crossconvergence: A new bounded topological presentation

[EN] We present crossconvergence, which commonly generalize bornology, preuniform convergence, orderconvergence, b-uniform filtration and grill-determined prenearness. The corresponding construct CCONV forms a strong topological universe, respectively quasitopos, in which quotients are stable under arbitrary products. We also discuss its enlargement to semicrossconvergence and precrossconvergence, respectively.