How to show a set is closed
What we need to do:
To show that the set S is closed, we need to take an arbitrary convergent sequence in S, and show that its limit belongs to S too.
What we say:
Let x_n be a sequence of elements of S which converge to a limit x_0 in S...
...and so x_0 is in S.
What we want to do:
We want to use the fact that x_n converges to x, together with additional properties of S that come from the particular problem, to show that x_0 belongs to S.
Example:
Question
Solution
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Analysis WebNotes by John Lindsay Orr.
Comments to the author:
jorr@math.unl.edu
All contents copyright (C) 1995 John L. Orr
University of Nebraska--Lincoln
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Last modified: June 13, 1995