Locally Regular Space - Examples and Properties

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:

    In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.
    Michel de Montaigne (1533–1592)

    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)