| space |
S000215 |
| property |
P000061 |
| value |
true |
| refs |
| mathse |
name |
4718866 |
Mysior plane is not realcompact |
|
|
The property {P6} was proven in {{mathse:4718866}}.
Note that if $V\subseteq X\setminus (\mathbb{R}\times {0})$ then $V = \bigcup_n V_n$ where $V_n = V\cap (X\setminus \mathbb{R}\times (-\frac{1}{n}, \frac{1}{n}))$ and $V_n$ are clopen, so that $U$ is a cozero set. If now $U\subseteq X$, let $V = X\setminus (U\cup \mathbb{R}\times {0})$, then $V$ is a cozero set and $V\cup U$ contains $X\setminus (\mathbb{R}\times {0})$ which is dense in $X$, so that $U\cup V$ is dense in $X$.