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I want to plot the following illustration in mathematica.

  1. First I need to plot a half open interval $(a,b]$ on a real line (ticks and labels are not needed).

  2. Then I need a piece of symmetric curve over "$b$" to indicate the neighborhood of $b$ with radius $\epsilon$.

I am not familiar with such plot. Can anyone provide some help. Thank you!

enter image description here

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8
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How about that:

o = {-0.5, 0};
e = {1.5, 0};
a = {0, 0};
b = {1, 0};
\[Epsilon] = 0.1;
Graphics[{
  Circle[b, \[Epsilon], {0, 180 Degree}],
  Line[{o, e}],
  Text["A", a, {0, 2}],
  Text["B", b, {0, 2}],
  Text["(", a],
  Text["]", b]
  }
 ]

enter image description here

This is just an illustrative example and I assume you can expand it to change the size, location, font, etc ...

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8
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Would a NumberLinePlot do the trick?

{a, b} = {7, 8}; eps = 0.05;
NumberLinePlot[{a < x <= b, b - eps < x < b + eps}, x, 
 Spacings -> {1, .3}, PlotStyle -> Directive[PointSize[Large]]]

enter image description here

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