Geodesic
Reznichenko's example is metalindel\"of
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 61-66

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We note that a pseudocompact space $X$ that was constructed by E. A. Reznichenko is hereditarily metalindelöf. Moreover, every (hereditarily) metalindelöf space $Y$ can be attached to $X$ (the size of $X$ can vary to accommodate $Y$) so that the resulting space is a (hereditarily) metalindelöf pseudocompact space that contains $Y$ as a closed subset. This example is much simpler than related constructions of a pseudocompact not compact space with a point-countable base that are due to S. Watson and D. B. Shakhmatov or a metalindelöf pseudocompact not compact space that is due to Ian Tree.
Keywords: metalindelöf, pseudocompact, closed embedding. 
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     author = {O. I. Pavlov},
     title = {Reznichenko's example is metalindel\"of},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {61--66},
     publisher = {mathdoc},
     number = {8},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_8_a5/}
}
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O. I. Pavlov. Reznichenko's example is metalindel\"of. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 61-66. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a5/