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- January 27th 2008, 09:04 AMrolylanemetric spaces
Hello

- January 27th 2008, 12:41 PMJaneBennet
The first one is straightforward. If , then

*x*is in an open ball*S*contained in*A*or one contained in*B*; in either case, and so .

For the second part, proving is equally straightforward.*x*is in an open ball*S*contained in and and .

For the reverse inclusion, let .

such that . Similarly . such that .

Now take .

Then proving that .

For the example, take the closed intervals and in . Then but and . - January 28th 2008, 08:29 AMrolylane
Thank you so much for your time and effort in replying to my query. I really am grateful.