Lindelöf space
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 (http://planetmath.org/T3Space) Lindelöf space is http://planetmath.org/node/1530normal.
sets (http://planetmath.org/F_sigmaSet) 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.
| Title | Lindelöf space |
| Canonical name | LindelofSpace |
| Date of creation | 2013-03-22 12:06:34 |
| Last modified on | 2013-03-22 12:06:34 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 11 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 54D20 |
| Related topic | SecondCountable |
| Related topic | Separable |
| Related topic | Compact |
| Related topic | LindelofTheorem |
| Related topic | CompactMetricSpacesAreSecondCountable |
| Related topic | ErnstLindelof |
| Defines | Lindelöf |
| Defines | Lindelöf property |