Examples and Properties
- Every locally regular T0 space is locally Hausdorff.
- A locally compact Hausdorff space is always locally regular.
- A regular space is always locally regular.
- A T1 space need not be locally regular as the set of all real numbers endowed with the cofinite topology shows.
Read more about this topic: Locally Regular Space
Famous quotes containing the words examples and/or properties:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)