Consider with the usual Euclidean metric d. Let $X$ = {$(x,\frac{1}{x})\in R^2 | x > 0$} ∪ {$(0, y) ∈R^2$ | y ≥ 0} ∪ {$(x, 0) ∈ R^2 | x ≥ 0$}. Then
which of the following statement is true ?
a. X is open but not closed.
b. X is neither open nor closed.
c. X is closed but not open.
d. X is open and closed.
I think in subspace topology X will be open set.... so option a) will corrects
Any hints /solution..Pliz help me
The correct answer is c). 'Open' and 'closed' refer to the topology of $\mathbb R^{2}$ not the subspace topology of $X$.