What question did this study set out to answer?

The aim is to explore the new semi-compact-open topology on quasicontinuous functions and its implications.

April 24, 2026Applied General TopologyOpen Access

Space of quasicontinuous functions with the topology of uniform convergence on semi-compacta

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This research introduces a new topology and examines properties of quasicontinuous functions, suggesting deeper connections within topology.

The aim is to explore the new semi-compact-open topology on quasicontinuous functions and its implications.
Introduce the semi-compact-open topology on function spaces.
Compare the topology of uniform convergence on semi-compacta with other topologies.
Investigate properties like induced functions and cardinal invariants.
The uniform convergence topology coincides with the semi-compact-open topology for quasicontinuous functions.
Connections between cardinal invariants and topological properties were established.
Ascoli-like properties are analyzed under the new topology framework.

Barman et al. (2026) studied this question.

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This research introduces a new topology and examines properties of quasicontinuous functions, suggesting deeper connections within topology.