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Search: MSC category 54D20 ( Noncompact covering properties (paracompact, Lindelof, etc.) )

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1. CMB 2011 (vol 56 pp. 203)

Tall, Franklin D.
 Productively LindelÃ¶f Spaces May All Be $D$ We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every LindelÃ¶f space is LindelÃ¶f, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz. Keywords:productively LindelÃ¶f, $D$-space, projectively $\sigma$-compact, Menger, HurewiczCategories:54D20, 54B10, 54D55, 54A20, 03F50

2. CMB 1998 (vol 41 pp. 245)

Yang, Lecheng
 The normality in products with a countably compact factor It is known that the product $\omega_1 \times X$ of $\omega_1$ with an $M_1$-space may be nonnormal. In this paper we prove that the product $\kappa \times X$ of an uncountable regular cardinal $\kappa$ with a paracompact semi-stratifiable space is normal if{f} it is countably paracompact. We also give a sufficient condition under which the product of a normal space with a paracompact space is normal, from which many theorems involving such a product with a countably compact factor can be derived. Categories:54B19, 54D15, 54D20

3. 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, boundaryCategories:54D20, 54B99, 54D10, 54D30