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separation axioms in a sentence

"separation axioms" in Chinese  

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  • See History of the separation axioms for more on this issue.
  • The proof relies on the use of the full separation axiom.
  • Compactness conditions together with preregularity often imply stronger separation axioms.
  • For more on this issue, see History of the separation axioms.
  • The properties T 1 and R 0 are examples of separation axioms.
  • Like all separation axioms, complete regularity is not preserved by taking Hausdorff.
  • The study of separation axioms is notorious for conflicts with naming conventions used.
  • Different authors restrict their attention to topological spaces that satisfy various separation axioms.
  • Includes such notions as convergence, separation axioms, metric spaces, dimension theory.
  • The partition topology provides an important example of the independence of various separation axioms.
  • It's difficult to see separation axioms in a sentence .
  • This is the weakest of the separation axioms.
  • These conditions are examples of separation axioms.
  • These are sometimes called " Tychonoff separation axioms ", after Andrey Tychonoff.
  • Some of these restrictions are given by the "'separation axioms " '.
  • Mathematicians decided to consider topological spaces more generally without the separation axiom which Felix Hausdorff originally formulated.
  • These conditions are separation axioms that are somewhat stronger than the more familiar Hausdorff axiom T 2.
  • This condition, called the "'T 0 condition "', is the weakest of the separation axioms.
  • The resulting topology does not satisfy the T 1 separation axiom, since all open sets have a non-empty intersection.
  • Second-countability is therefore a rather restrictive property on a topological space, requiring only a separation axiom to imply metrizability.
  • For example, the definition given by Felix Hausdorff in 1914 is equivalent to the modern definition plus the Hausdorff separation axiom.
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