Questions tagged [realcompact-spaces]

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T. Hanaoka's "Note on c-realcompact spaces and mappings"

I need T. Hanaoka's article Note on c-realcompact spaces and mappings, Memoirs of the Osaka Kyoiku Univ., Ser. Ill, 26 (1977), 55-58. Can anyone find it for me? http://ir.lib.osaka-kyoiku.ac.jp/dspace/...
Mehmet Onat's user avatar
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Mysior plane is not realcompact

Let $X = \mathbb{R}^2$ with $(x, y)\in X$ for $y\neq 0$ isolated and $(x, 0)$ having neighbourhood basis of the form $$U_n(x) = \{(x, y) : y\in (-1/n, 1/n)\}\cup \{(x+y+1, y) : 0 < y < 1/n\}\cup ...
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1 vote
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A question about realcompact spaces

Let $X$ be completely regular space, $\beta X$ be Stone-Čech compactification of $X$, and $\upsilon X$ be Hewitt realcompactification of $X$. Then $X\subset \upsilon X\subset \beta X$. If the ...
Mehmet Onat's user avatar
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2 votes
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A question about a realcompact space and upper semicontinuous function

Nancy Dykes says in the proof of Theorem 3.4 in her article Generalizations of realcompact spaces that by a result of John Mack, if for every $p\in \beta X\setminus X$ there exists a nonnegative upper ...
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