Yang Ming-quan
Abstract
The following is proved: Let X be the inverse limit of an inverse system ｛Xα, παβ, Λ｝and λthe cardinal number of .Λ Suppose each projections πα: X→Xαis an open and onto map and X is -λparacompact. If each Xαis -σOrthocom- pect, then X is σ-Orthocompect. Moreover, the analogous results for hereditarily σ-Orthocompact are obtained.
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The following is proved: Let X be the inverse limit of an inverse system ｛Xα, παβ, Λ｝and λthe cardinal number of .Λ Suppose each projections πα: X→Xαis an open and onto map and X is -λparacompact. If each Xαis -σOrthocom- pect, then X is σ-Orthocompect. Moreover, the analogous results for hereditarily σ-Orthocompact are obtained.
Key concepts: Inverse limit, Inverse, Limit (mathematics), Inverse system, Paracompact space, Mathematics, Space (punctuation), Mathematical analysis