![real analysis - Why must the countable sets shown in this example be closed? - Mathematics Stack Exchange real analysis - Why must the countable sets shown in this example be closed? - Mathematics Stack Exchange](https://i.stack.imgur.com/YHxd0.png)
real analysis - Why must the countable sets shown in this example be closed? - Mathematics Stack Exchange
![SOLVED: Which one is false? (A) If the set A contains all its limit points, then it is closed (B) If the set A € Ris compact; then the set f( A) SOLVED: Which one is false? (A) If the set A contains all its limit points, then it is closed (B) If the set A € Ris compact; then the set f( A)](https://cdn.numerade.com/ask_images/c9fbdacaba944d50a93d3b8c61c54ce4.jpg)
SOLVED: Which one is false? (A) If the set A contains all its limit points, then it is closed (B) If the set A € Ris compact; then the set f( A)
![real analysis - every infinite subset of a metric space has limit point => metric space compact? - Mathematics Stack Exchange real analysis - every infinite subset of a metric space has limit point => metric space compact? - Mathematics Stack Exchange](https://i.stack.imgur.com/tHIo7.png)
real analysis - every infinite subset of a metric space has limit point => metric space compact? - Mathematics Stack Exchange
![SOLVED: (a)Construct a nonempty compact subset of R whose limit points form a countable set. (a)What sequences converge in a discrete metric space? SOLVED: (a)Construct a nonempty compact subset of R whose limit points form a countable set. (a)What sequences converge in a discrete metric space?](https://cdn.numerade.com/ask_previews/a876a3c4-7f65-4ce6-9577-cf49a56df83d_large.jpg)
SOLVED: (a)Construct a nonempty compact subset of R whose limit points form a countable set. (a)What sequences converge in a discrete metric space?
![DEFINITION -SEQUENTIALLY COMPACT | THEOREM - X IS LIMIT POINT COMPACT THEN X IS SEQUENTIALLY COMPACT - YouTube DEFINITION -SEQUENTIALLY COMPACT | THEOREM - X IS LIMIT POINT COMPACT THEN X IS SEQUENTIALLY COMPACT - YouTube](https://i.ytimg.com/vi/64nH6f03SC4/hqdefault.jpg)
DEFINITION -SEQUENTIALLY COMPACT | THEOREM - X IS LIMIT POINT COMPACT THEN X IS SEQUENTIALLY COMPACT - YouTube
![general topology - Prove that a metric space in which every infinite subset has a limit point is separable. - Mathematics Stack Exchange general topology - Prove that a metric space in which every infinite subset has a limit point is separable. - Mathematics Stack Exchange](https://i.stack.imgur.com/OhGi4.png)
general topology - Prove that a metric space in which every infinite subset has a limit point is separable. - Mathematics Stack Exchange
![real analysis - Compact subset of $\mathbb{R}^1$ with countable limit points - Mathematics Stack Exchange real analysis - Compact subset of $\mathbb{R}^1$ with countable limit points - Mathematics Stack Exchange](https://i.stack.imgur.com/LzhC2.jpg)