Abstract
We introduce the notion of mixed weak (μ,ν1ν2)-continuity between a generalized topology μ and two generalized topologies ν1, ν2. We characterize such continuity in terms of mixed generalized open sets: (ν1,ν2)′-semiopen sets, (ν1,ν2)′-preopen sets, (ν1,ν2)-preopen sets [2], (ν1,ν2)′-β′-open sets and θ(ν1,ν2)-open sets [3]. In particular, we show that for a given mixed weakly (μ,ν1ν2)-continuous function, if the codomain of the given function is mixed regular (=(ν1,ν2)-regular), then the function is also (μ,ν1)-continuous.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357.
Á. Császár, Mixed constructions for generalized topologies, Acta Math. Hungar., 122 (2009), 153–159.
Á. Császár and E. Makai Jr., Further remarks on δ- and θ-modificatons, Acta Math. Hungar., 123 (2009), 223–228.
W. K. Min, Weak continuity on generalized topological spaces, Acta Math. Hungar., 124 (2009), 73–81.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Min, W.K. Mixed weak continuity on generalized topological spaces. Acta Math Hung 132, 339–347 (2011). https://doi.org/10.1007/s10474-011-0078-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-011-0078-2