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Suppose $X=\cup K_n$ is a topological space, $K_n$ is a metrizable subspace in $X$ for every $n \in \omega$, then $X$ is a metrizable space? In metrizable spacespaces, compactness is equivalent to $\sigma$-compactness? One more: Is pseudocompactness hereditary with respect to $\sigma$-compact subspace? |
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Suppose $X=\cup K_n$ is a topological space, $K_n$ is a metrizable subspace in $X$ for every $n \in \omega$, then $X$ is a metrizable space? In metrizable space, compactness is equivalent to $\sigma$-compactness? One more: Is pseudocompactness hereditary with respect to $\sigma$-compact subspace? |
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Suppose $X=\cup K_n$ is a topological space, $K_n$ is a metrizable subspace in $X$ for every $n \in \omega$, then $X$ is a metrizable space? In metrizable space, $compactness$ compactness is equivalent to $\sigam$-compact?\sigma$-compactness? |
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