Crossconvergence: A new bounded topological presentation
Submitted: 2026-01-26
|Accepted: 2026-05-01
|Published: 2026-06-05
Copyright (c) 2026 Dieter Leseberg, Zohreh Vaziry
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
continuity structures, generalized continuity structures, convenient topology, bounded topology, quasitopos, strong topological universe
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Abstract:
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.
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