4 problems

Let \rm\sffamily CC$_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $\operatorname{id}\times f$ for…

Let \rm\sffamily CC$_2$ denote connected choice for non-empty connected closed subsets of $[0,1]^2$. For a multi-valued operation $f$, write $f\times f$ for two parallel ins…

Let \rm\sffamily CC$_2$ be connected choice for non-empty connected closed subsets of $[0,1]^2$, and let \rm\sffamily C$_{[0,1]}$ be closed choice on the unit interva…

Let ${\rm UC}_X$ denote the unique closed choice operation on a represented Hausdorff space $X$, and let ${\rm C}_X$ denote closed choice on $X$. For Baire space…