= Gluing three-balls along a boundary disk
Two <piecewise linear balls> of dimension three glued along a common <boundary> <disk> form another <piecewise linear ball>. The <Schoenflies theorem> identifies each <boundary> pair with a <sphere> and a hemisphere. Coning the resulting <boundary> <homeomorphisms> extends them over the balls, which then become the two halves of a standard ball. The same argument shows that removing a ball attached along one <boundary> <disk> leaves a ball.
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