Forbidden rectangles in compacta
Copyright policy )Forbidden rectangles in compacta
We establish negative results about "rectangular" local bases in compacta. For example, there is no compactum where all points have local bases of cofinal type ��x ��_2. For another, the compactum ����has no nontrivially rectangular local bases, and the same is consistently true of ����\ ��: no local base in ����has cofinal type ��x c if ��< m_{��-n-linked} for some n in [1,��). Also, CH implies that every local base in ����\ ��has the same cofinal type as one in ����. We also answer a question of Dobrinen and Todorcevic about cofinal types of ultrafilters: the Fubini square of a filter on ��always has the same cofinal type as its Fubini cube. Moreover, the Fubini product of nonprincipal P-filters on ��is commutative modulo cofinal equivalence.
15 pages
- Texas A&M International University United States
Cellularity, compact, Base properties of topological spaces, General Topology (math.GN), Cofinal type, Mathematics - Logic, Compact, 54A25 (Primary) 03E04, 54D80, 54D70 (Secondary), Fubini product, Ordered sets and their cofinalities; pcf theory, homogeneous, cellularity, Ultrafilter, FOS: Mathematics, Homogeneous, Cardinality properties (cardinal functions and inequalities, discrete subsets), Special constructions of topological spaces (spaces of ultrafilters, etc.), Logic (math.LO), ultrafilter, cofinal type, Mathematics - General Topology
Cellularity, compact, Base properties of topological spaces, General Topology (math.GN), Cofinal type, Mathematics - Logic, Compact, 54A25 (Primary) 03E04, 54D80, 54D70 (Secondary), Fubini product, Ordered sets and their cofinalities; pcf theory, homogeneous, cellularity, Ultrafilter, FOS: Mathematics, Homogeneous, Cardinality properties (cardinal functions and inequalities, discrete subsets), Special constructions of topological spaces (spaces of ultrafilters, etc.), Logic (math.LO), ultrafilter, cofinal type, Mathematics - General Topology
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