Elsevier

Topology and its Applications

Volume 154, Issue 2, 15 January 2007, Pages 469-475
Topology and its Applications

The D-property of some Lindelöf spaces and related conclusions

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Abstract

It is shown that the space Cp(τω) is a D-space for any ordinal number τ, where τω={ατ:cf(α)ω}. This conclusion gives a positive answer to R.Z. Buzyakova's question. We also prove that another special example of Lindelöf space is a D-space. We discuss the D-property of spaces with point-countable weak bases. We prove that if a space X has a point-countable weak base, then X is a D-space. By this conclusion and one of T. Hoshina's conclusion, we have that if X is a countably compact space with a point-countable weak base, then X is a compact metrizable space. In the last part, we show that if a space X is a finite union of θ-refinable spaces, then X is a αD-space.

MSC

54C35
54D20
54F05

Keywords

D-space
Cp(τω)
Lindelöf space
θ-refinable space
Weak base

Cited by (0)

Research supported by Beijing Natural Science Foundation 1062002.