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Feb 7, 2022 at 13:59 comment added Nick L Right, thanks. Together with Will Sawin's answer that seems to cover every case.
Feb 7, 2022 at 13:49 comment added მამუკა ჯიბლაძე By the way, obviously there is no retraction for $|K|>1$ since in that case $\mathbb{CP}^1\setminus K$ acquires a nontrivial fundamental group while $\mathbb{CP}^2\setminus K$ remains simply connected
Feb 7, 2022 at 9:36 history answered Nick L CC BY-SA 4.0