2015/04/30 by Plewik, Szymon, Walczyńska, Marta
#54G12 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1504.08130
Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpiński and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric σ-discrete spaces. Some related topics are also explored. For example: For each infinite cardinal number \frak m, there exist 2\frak m many non-homeomorphic metric scattered spaces of the cardinality \frak m ; If X ⊆ ω1 is a stationary set, then the poset formed from dimensional types of subspaces of X contains uncountable anti-chains and uncountable strictly descending chains.