Topology Proceedings 30 No. 1 (2006), pp. 355-365

Monotonically D-Spaces

Strashimir G. Popvassilev and John E. Porter

Call X monotonically D if we can assign a closed discrete D(U) to every open neighborhood assignment U={U(x):x ∈ X} in such a way that X=∪{U(x):x ∈ D(U)} and D(U) ⊆ D(V) if V(x) ⊆ U(x) for all x. The Michael line and countable, first-countable spaces are monotonically D. The Sorgenfrey line, the unit interval, and w₁+1 are not.

Keywords: generalized left separated, GLS, Michael line, monotonically D-spaces, non-Archimedean, w₁+1, Sorgenfrey line, unit interval

Mathematics Subject Classification: 54D20 54D30 54F05

Document formats: PDF file 198.0 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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