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Lindelöf space∗
yark†
2013-03-21 13:04:16
Definition
A topological space is said to be Lindelöf if every open cover has a countable
subcover.
Notes
A second-countable space is Lindelöf. A compact space is Lindelöf.
A regular Lindelöf space is normal.
Fσ sets in Lindelöf spaces are Lindelöf. Continuous images of Lindelöf spaces
are Lindelöf.
A Lindelöf space is compact if and only if it is countably compact.
∗ hLindelofSpacei created: h2013-03-21i by: hyarki version: h31226i Privacy setting: h1i
hDefinitioni h54D20i
† 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.
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