MHB About open sets in a metric space.

[eraldcoil1]

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.

 

[caffeinemachine]

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.