Is every paracompact topology contained in a maximal paracompact topology?

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If $(X,tau)$ is a paracompact, is there a topology $tau'supseteq tau$ such that $(X,tau')$ is still paracompact, and $tau'$ is maximal with respect to $subseteq$ and paracompactness?






gn.general-topology paracompactness







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    If $(X,tau)$ is a paracompact, is there a topology $tau'supseteq tau$ such that $(X,tau')$ is still paracompact, and $tau'$ is maximal with respect to $subseteq$ and paracompactness?






    gn.general-topology paracompactness







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      If $(X,tau)$ is a paracompact, is there a topology $tau'supseteq tau$ such that $(X,tau')$ is still paracompact, and $tau'$ is maximal with respect to $subseteq$ and paracompactness?






      gn.general-topology paracompactness







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      If $(X,tau)$ is a paracompact, is there a topology $tau'supseteq tau$ such that $(X,tau')$ is still paracompact, and $tau'$ is maximal with respect to $subseteq$ and paracompactness?






      gn.general-topology paracompactness




      gn.general-topology paracompactness






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      asked 2 hours ago









      Dominic van der Zypen

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          Any discrete space is paracompact, since the family of singletons is locally finite and an open refinement of every open cover. Put $tau'=mathcalP(X)$. Then the discrete space $(X,tau')$ is paracompact, and $tau'$ is maximal with respect to inclusion and paracompactness.






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            Any discrete space is paracompact, since the family of singletons is locally finite and an open refinement of every open cover. Put $tau'=mathcalP(X)$. Then the discrete space $(X,tau')$ is paracompact, and $tau'$ is maximal with respect to inclusion and paracompactness.






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              Any discrete space is paracompact, since the family of singletons is locally finite and an open refinement of every open cover. Put $tau'=mathcalP(X)$. Then the discrete space $(X,tau')$ is paracompact, and $tau'$ is maximal with respect to inclusion and paracompactness.






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                Any discrete space is paracompact, since the family of singletons is locally finite and an open refinement of every open cover. Put $tau'=mathcalP(X)$. Then the discrete space $(X,tau')$ is paracompact, and $tau'$ is maximal with respect to inclusion and paracompactness.






                share|cite|improve this answer












                Any discrete space is paracompact, since the family of singletons is locally finite and an open refinement of every open cover. Put $tau'=mathcalP(X)$. Then the discrete space $(X,tau')$ is paracompact, and $tau'$ is maximal with respect to inclusion and paracompactness.







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                answered 54 mins ago









                Philipp Lampe

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