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)

    The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.
    John Locke (1632–1704)