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Article
Thin-Type Dense Sets and Related Properties
Topology and Its Applications
  • Jennifer D. Hutchison, Cedarville University
  • G. Gruenhage
Document Type
Article
Publication Date
10-1-2011
Abstract
We build on Gruenhage, Natkaniec, and Piotrowskiʼs study of thin, very thin, and slim dense sets in products, and the related notions of (NC) and (GC) which they introduced. We find examples of separable spaces X such that Formula Not Shown has a thin or slim dense set but no countable one. We characterize ordered spaces that satisfy (GC) and (NC), and we give an example of a separable space which satisfies (GC) but not witnessed by a collection of finite sets. We show that the question of when the topological sum of two countable strongly irresolvable spaces satisfies (NC) is related to the Rudin–Keisler order on βω. We also introduce and study the concepts of <κ-thin and superslim dense sets.
Keywords
  • Dense set; Thin set; Slim set; Superslim set; (GC); (NC); Ordered space
Citation Information
Jennifer D. Hutchison and G. Gruenhage. "Thin-Type Dense Sets and Related Properties" Topology and Its Applications Vol. 158 Iss. 16 (2011) p. 2174 - 2183
Available at: http://works.bepress.com/jennifer_hutchison/1/