Questions tagged [realcompact-spaces]
The realcompact-spaces tag has no usage guidance.
4
questions
0
votes
0
answers
64
views
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/...
4
votes
1
answer
222
views
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 ...
1
vote
1
answer
336
views
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 ...
2
votes
1
answer
110
views
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 ...