MHB About open sets in a metric space.

eraldcoil1
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Let $$(E=]-1,0]\cup\left\{1\right\},d) $$ metric space with $$d$$ metric given by $$d(x,y)=|x-y|$$, and $$||$$absolute value.

How I can find open sets of E explicitly?
Thanks in advance.
 
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eraldcoil said:
Let $$(E=]-1,0]\cup\left\{1\right\},d) $$ metric space with $$d$$ metric given by $$d(x,y)=|x-y|$$, and $$||$$absolute value.

How I can find open sets of E explicitly?
Thanks in advance.
Can you please post your progress on this question or anything you have tried? Start with defining open sets in an arbitrary metric space.
 
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