A Note on Θ-closed Sets and Inverse Limits
نویسنده
چکیده
For every Hausdorff space X the space XΘ is introduced. If X is H-closed, then XΘ is a quasy-compact T1-space. If f : X → Y is a mapping, then there exists the mapping fΘ : XΘ → YΘ. We say that a mapping f : X → Y is Θ-closed if fΘ is a closed mapping. If X and Y are H-closed and if f : X → Y is a HJ-mapping, then fΘ is Θ-closed. Let X = {Xa, pab, A} be an inverse system of H-closed spaces Xa and Θ-closed bonding mappings fab. If Xa are non-empty spaces, then X = limX is non-empty. If the bonding mappings pab are HJ, then X = limX is non-empty and H-closed
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