Probabilistic Topologies Induced by L-Fuzzy Uniformities.
If a metrizable space is dense in a metrizable space , then is called a metric extension of . If and are metric extensions of and there is a continuous map of into keeping pointwise fixed, we write . If is noncompact and metrizable, then denotes the set of metric extensions of , where and are identified if and , i.e., if there is a homeomorphism of onto keeping pointwise fixed. is a large complicated poset studied extensively by V. Bel’nov [The structure of...
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .