Geodesic
$C^*$-points vs $P$-points and $P^\flat$-points
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 2, pp. 245-259.

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In a Tychonoff space $X$, the point $p\in X$ is called a $C^*$-point if every real-valued continuous function on $C\smallsetminus \{p\}$ can be extended continuously to $p$. Every point in an extremally disconnected space is a $C^*$-point. A classic example is the space ${\bf W}^*=\omega_1+1$ consisting of the countable ordinals together with $\omega_1$. The point $\omega_1$ is known to be a $C^*$-point as well as a $P$-point. We supply a characterization of $C^*$-points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a $C^*$-point. This process leads to many interesting new discoveries.
DOI : 10.14712/1213-7243.2022.015
Classification : 54D15, 54F05, 54G10
Keywords: ring of continuous functions; $C^*$-embedded; $P$-point 
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Martinez, Jorge; McGovern, Warren Wm. $C^*$-points vs $P$-points and $P^\flat$-points. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 2, pp. 245-259. doi : 10.14712/1213-7243.2022.015. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.015/

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