- #1
emob2p
- 56
- 1
Homework Statement
I am asked to show that T=[particular point topology on R^2 ((0,0) being the particular point)] is equal to T'=[topology on R^2 from taking the product of R in the particular point topology (0 being particular point) with itself].
The Attempt at a Solution
I'm pretty sure the book is wrong and this problem can't be solved. Consider the set {(0,0),(1,1)}. This is open in T, but I cannot see how this is open in T' since for the point (1,1) we cannot construct an open set that contains (1,1) but is contained in {(0,0),(1,1)}. The closest we can get is {0,1}x{0,1}={(0,0),(1,0),(0,1),(1,1)}. Am I correct, or am I missing something?