Abstract
We prove that the (transitive) infimum of the Pervin quasi- uniformity with a compatible (transitive) quasi-uniformity V always exists, more- over it equals the coarsest element of the quasi-proximity class of the quasi- proximity which is inducedby V . As a consequence, it is shown that in general the compatible quasi-uniformities do not constitute a distributive lattice.
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Losonczi, A. NOTES ON THE COARSEST ELEMENT OF pi. Acta Mathematica Hungarica 92, 137–141 (2001). https://doi.org/10.1023/A:1013764313587
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DOI: https://doi.org/10.1023/A:1013764313587