Question: 1. Show that (0, 1) U (2,3) is an open set in R. 2. Show that (0,1] is not an open set in R.

1. Show that (0, 1) U (2,3) is an open set in R. 2. Show that (0,1] is not an open set in R. 3. Show that [0, 1] = R \ [0, 1] = {x R x [0,1]} is an open set in R. 4. Show that the whole line R is an open set in itself.

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