Section 17: Problem 14 Solution

Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

In the finite complement topology on $\mathbb{R}$ , to what point or points does the sequence $x_{n}=1/n$ converge?

For any point and any its neighborhood (which in the finite complement topology is $\mathbb{R}$ minus a finite number of points) there is only finite number of points in the sequence that may be not in the neighborhood (all points of the sequence are different), so the sequence converges to every point in $\mathbb{R}_{fc}$ .

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Section 17: Problem 14 Solution

Section 17: Problem 14 Solution