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Search: All articles in the CMB digital archive with keyword $D$-space

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1. CMB 2011 (vol 56 pp. 203)

Tall, Franklin D.
Productively Lindelöf Spaces May All Be $D$
We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every Lindelöf space is Lindelöf, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.

Keywords:productively Lindelöf, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz
Categories:54D20, 54B10, 54D55, 54A20, 03F50

2. CMB 1997 (vol 40 pp. 395)

Boudhraa, Zineddine
$D$-spaces and resolution
A space $X$ is a $D$-space if, for every neighborhood assignment $f$ there is a closed discrete set $D$ such that $\bigcup{f(D)}=X$. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a $D$-space. In particular, if a space $X$ is resolved at each $x\in X$ into a $D$-space $Y_x$ by continuous mappings $f_x\colon X-\{{x}\} \rightarrow Y_x$, then the resolution is a $D$-space if and only if $\bigcup{\{{x}\}}\times \Bd(Y_x)$ is a $D$-space.

Keywords:$D$-space, neighborhood assignment, resolution, boundary
Categories:54D20, 54B99, 54D10, 54D30

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