Geodesic
Some Remarks on Almost Menger Spaces and Weakly Menger Spaces
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 193

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A space $X$ is \emph{almost Menger (weakly Menger)} if for each sequence $(\U_n:n\in\mathbb N)$ of open covers of $X$ there exists a sequence $(\mathcal V_n:n\in\mathbb N)$ such that for every $n\in\mathbb N$, $\mathcal V_n$ is a finite subset of $\U_n$ and $\bigcup_{n\in\mathbb N}\bigcup\big\{\overline{V}:V\in\mathcal V_n\big\}=X$ (respectively, $\overline{\bigcup_{n\in\mathbb N}\bigcup\{V:V\in\mathcal V_n\}}=X$). We investigate the relationships among almost Menger spaces, weakly Menger spaces and Menger spaces, and also study topological properties of almost Menger spaces and weakly Menger spaces.
DOI : 10.2298/PIM150513031S
Classification : 54D20 54A35
Keywords: Menger spaces, almost Menger spaces, weakly Menger spaces 
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     journal = {Publications de l'Institut Math\'ematique},
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Yan-Kui Song. Some Remarks on Almost Menger Spaces and Weakly Menger Spaces. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 193 . doi: 10.2298/PIM150513031S

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