separation axioms in a sentence
SentencesMobile
- 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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