Box Topology - Properties

Properties

Box topology on Rω:

  • The box topology is completely regular
  • The box topology is neither compact nor connected
  • The box topology is not first countable
  • The box topology is not separable
  • The box topology is paracompact (and hence normal and completely regular) if the continuum hypothesis is true

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    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.
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