More on Uniform Paracompactness in Pointfree Topology
AbstractWe revisit uniformly paracompact uniform frames and show that, in analogy with their spatial counterparts, they have a characterisation in terms of a “completeness property”. Namely, they are precisely those in which every weakly Cauchy filter clusters. We also give another characterisation in terms of the Čech-Stone compactification of the underlying frame. By tweaking the definition of uniformly paracompact frames, we define uniformly para-Lindelöf frames (analogously to same-named uniform spaces) and characterise them in terms of the Lindelöf coreflection of the underlying frame. This latter characterisation has no spatial counterpart.
2021 ◽
Vol 2021
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pp. 29-34
1979 ◽
Vol 46
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pp. 125-149
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1977 ◽
Vol 35
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pp. 408-409
1969 ◽
Vol 27
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pp. 12-13
1973 ◽
Vol 31
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pp. 324-325
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1988 ◽
Vol 46
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pp. 1012-1015