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On 3-topological version of $$\Theta$$-regularity. (English) Zbl 0991.54037
Summary: We modify the concept of $$\theta$$-regularity for spaces with two and three topologies. The new, more general property is fully preserved by sums and products. Using some bitopological reductions of this property, E. Michael’s theorem for several variants of bitopological paracompactness is proved [Proc. Am. Math. Soc. 4, 831-838 (1953; Zbl 0052.18701)].

##### MSC:
 54E55 Bitopologies 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
##### Keywords:
$$\theta$$-regularity; paracompactness
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