Partitioning bases of topological spaces
Copyright policy )Partitioning bases of topological spaces
We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a T_3 Lindel��f topology can be partitioned into two bases while there exists a consistent example of a first countable, 0-dimensional, Hausdorff space of size continuum and weight ��_1 which admits a point countable base without a partition to two bases. Several related results are proved and the paper finishes with a list of open problems.
26 pages, revised, submitted to CMUC
Consistency and independence results in general topology, QA Mathematics / matematika, General Topology (math.GN), FOS: Mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, base, 54A35, 03E35, 54A25, partition, resolvable, Mathematics - General Topology
Consistency and independence results in general topology, QA Mathematics / matematika, General Topology (math.GN), FOS: Mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, base, 54A35, 03E35, 54A25, partition, resolvable, Mathematics - General Topology
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