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- W2019693853 abstract "1. Stone2 has proved that a space is fully normal T, if and only if it is paracompact T2. If throughout his proof T, is deleted and T2 is replaced by T4 (normality), we obtain that a space is fully normal if and only if it is paracompact T4. In this note we prove that T2 can also be replaced by any one of the following: T21. Every two points with disjoint closures have disjoint neighborhoods. T3'. For each point x and neighborhood U of x there is a neighborhood V of x whose closure is contained in U. LT4. Every point has a neighborhood whose closure is normal. Moreover, we shall also study a natural decomposition of a space with certain properties and prove that a space is paracompact T4 if and only if it has a retract which is paracompact T2 and meets every non-null closed set. The following terminology will be used. PROPERTY *. If x, y, z are any three points such that 90Nys 0 and VC2$0, then 9n2p0. PROPERTY **. Every point has a compact closure. We remark that" @default.
- W2019693853 created "2016-06-24" @default.
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- W2019693853 date "1954-02-01" @default.
- W2019693853 modified "2023-09-24" @default.
- W2019693853 title "On paracompact spaces" @default.
- W2019693853 doi "https://doi.org/10.1090/s0002-9939-1954-0062418-0" @default.
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