Sorgenfrey half-open plane
It is interesting to note that, even though the Sorgenfrey line enjoys the Lindelöf property (http://planetmath.org/lindelofspace), the Sorgenfrey plane does not. To see this, one can note that the line is a closed subset in this topology and that the induced topology on this line is the discrete topology. Since the Lindelöf property is weakly hereditary, the discrete topology on the real line would have to be Lindelöf if the Sorgenfrey plane topology were Lindelöf. However, the discrete topology on an uncountable set can never have the Lindelöf property, so the Sorgenfrey topology cannot have this property either.
|Title||Sorgenfrey half-open plane|
|Date of creation||2014-11-06 13:51:15|
|Last modified on||2014-11-06 13:51:15|
|Last modified by||pahio (2872)|
|Synonym||Sorgenfrey’s half-open square topology|