William Elliot wrote:

If the union of a countable pairwise disjoint collection of

bounded, simply connected open sets is removed from the real

plain, is the result path connected?

If the union of a countable pairwise disjoint collection of

simply connected compact sets with non-empty interior, is

removed from the real plain, is the result path connected?

I don't know the answers, but I would see if I could use a tool like

the

function y=sin(1/x), to achieve a "negative" result. "Fun" problem!

-Bill

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