Path connected subsets
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Give proofs or counter-example for the following statements:
i)If X and Y are path connected subsets of Z and X/Y ( X intersection Y)
is non empty then X/Y is path connected.
ii) If X and Y are path connected subsets of Z the X/Y(union) is
path-connected.
iii)If X and Y are path connected subsets of Z and X/Y ( X intersection Y)
is non empty then X/Y(union) is path connected.
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Solution Summary
This solution is comprised of a detailed explanation to give proofs or counter-example for the following statements.
Solution Preview
i) False. Take as X and Y as the two halves of a circle, that intersect
in 2 distinct points.
ii) False. Take X = {0}, Y = {1} in R.
iii) ...
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