Initial Topologies

Some articles on initial topologies, topologies:

Tychonoff Space - Properties - Preservation
... property are well-behaved with respect to initial topologies ... Specifically, complete regularity is preserved by taking arbitrary initial topologies and the Tychonoff property is preserved by taking point-separating initial topologies ... Like all separation axioms, completely regularity is not preserved by taking final topologies ...

Famous quotes containing the word initial:

    No punishment has ever possessed enough power of deterrence to prevent the commission of crimes. On the contrary, whatever the punishment, once a specific crime has appeared for the first time, its reappearance is more likely than its initial emergence could ever have been.
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