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Frontier points proof

  1. Oct 18, 2013 #1

    ppy

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    3.4. Let E[itex]\in[/itex]  R. Prove or disprove the following statements:
    (i) if a[itex]\in[/itex]E and b[itex]\in[/itex]E[itex]^{c}[/itex] = ℝ\E and a < b then [a ,b] [itex]\cap[/itex]∂E IS NOT EQUAL TO ∅.
    (ii) if a[itex]\in[/itex]E and b[itex]\in[/itex]E[itex]^{c}[/itex] = ℝ\E and a < b then (a ,b) [itex]\cap[/itex]∂E IS NOT EQUAL TO ∅.


    I am really stuck I know that the frontier of a set is when a sequence in E and a sequence in E[itex]^{c}[/itex] converge to the same limit.
     
  2. jcsd
  3. Oct 18, 2013 #2

    ppy

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    I am able to show this from drawing a sketch but how can I do it without a drawing?
     
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