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Q1, Does a metrizable space $X$ with $e(X)=\omega$ (i.e., it has countable extent) which is not lindelof exist? Q2, Let $X$ be the one point lindefication of a discret space of cardinality $\omega_1$ and $Y$ is any Lindelof space. Is $X \times Y$ always Lindelof? Thanks for any help. |
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A question on metrizable spaceDoes a metrizable space $X$ with $e(X)=\omega$ (i.e., it has countable extent) which is not lindelof exist? Thanks for any help.
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