Every uncountable set in a 2nd countable space has a limit point.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Could you explain how to show 5.11 in easiest possible way(in very detail)?

**Definition:** A space \( X \) is 2<sup>nd</sup> countable if and only if \( X \) has a countable basis.

**Theorem 5.11:** Every uncountable set in a 2<sup>nd</sup> countable space has a limit point.
Transcribed Image Text:**Definition:** A space \( X \) is 2<sup>nd</sup> countable if and only if \( X \) has a countable basis. **Theorem 5.11:** Every uncountable set in a 2<sup>nd</sup> countable space has a limit point.
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