Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PDF
Document related concepts
Transcript
weakly countably compact∗ yark† 2013-03-21 13:04:37 A topological space X is said to be weakly countably compact (or limit point compact) if every infinite subset of X has a limit point. Every countably compact space is weakly countably compact. The converse is true in T1 spaces. A metric space is weakly countably compact if and only if it is compact. An easy example of a space X that is not weakly countably compact is any infinite set with the discrete topology. A more interesting example is the countable complement topology on an uncountable set. ∗ hWeaklyCountablyCompacti created: h2013-03-21i by: hyarki version: h31234i Privacy setting: h1i hDefinitioni h54D30i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
