(220:0.5);

(0,0) circle(0.5cm);

at (5:0.60)[$x_0^i$]{}; at (60:0.60)[$p$]{}; at (115:0.60)[$x'^i_0$]{};

at (238:0.60)[$x_1^i$]{}; at (210:0.60)[$q$]{}; at (265:0.60)[$x'^i_1$]{};

(10:0.60) arc (10:55:0.60); (65:0.60) arc (65:110:0.60);

(260:0.60) arc (260:243:0.60); (233:0.60) arc (233:215:0.60);

(210:0.5) node\[fill=white,circle,inner sep=0.065cm\] circle (0.02cm); (60:0.5) node\[fill=white,circle,inner sep=0.065cm\] circle (0.02cm);

(10:0.48) – (10:0.52); (257:0.48) – (257:0.52); (10:0.5) .. controls (10:0.2) and (257:0.2) .. (257:0.5);

(30:0.48) – (30:0.52); (238:0.48) – (238:0.52); (30:0.5) .. controls (30:0.1) and (238:0.1) .. (238:0.5);

(45:0.48) – (45:0.52); (225:0.48) – (225:0.52); (45:0.5) .. controls (45:0.1) and (225:0.1) .. (225:0.5);

(55:0.48) – (55:0.52); (215:0.48) – (215:0.52); (55:0.5) .. controls (55:0.1) and (215:0.1) .. (215:0.5);

(115:0.48) – (115:0.52); (265:0.48) – (265:0.52); (115:0.5) .. controls (115:0.3) and (265:0.3) .. (265:0.5);

(95:0.48) – (95:0.52); (245:0.48) – (245:0.52); (95:0.5) .. controls (95:0.3) and (245:0.3) .. (245:0.5);

(80:0.48) – (80:0.52); (230:0.48) – (230:0.52); (80:0.5) .. controls (80:0.3) and (230:0.3) .. (230:0.5);

(70:0.48) – (70:0.52); (220:0.48) – (220:0.52); (70:0.5) .. controls (70:0.3) and (220:0.3) .. (220:0.5);

The letters “PC” stands for “precovering”.

[PC2:]{}

If there is a sequence $\{x^i_0, x^i_1\}_{i \in {\mathbb{Z}}_{\geqslant 0}}$ from ${\mathscr{X}}$ with $x^i_0 \to p$ from below and $x^i_1 \to q$ from below with $p \neq q$, then there is a sequence $\{x'^i_0, x'^i_1\}_{i \in {\mathbb{Z}}_{\geqslant 0}}$ from ${\mathscr{X}}$ with $x'^i_0 \to p$ 