Consider the set of real numbers R, and define for any point x ER and a positive real number e, an open interval B.(x) centered at x and of radius e as B₁(x) = {y ≤R: |x-y| < e}. (a) Use the open interval notion defined above to formulate the e- & continuity of the function f: R → R at a point z E R. (b) Using the above notion of open interval, when do we say a subset G of the set of real numbers is open? (c) Write down the three properties of the class of all open subsets of R.

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