| NOUN | a topological space | topological spaces |
| SYNO | mathematical space | topological space |
NOUN article.ind sg | pl
24 Übersetzungen
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Anwendungsbeispiele Englisch
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- It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal topological space, where the Tietze extension theorem guarantees that a continuous function on a closed subset always extends to the ambient topological space.
- One such generalization is that a topological space is "sequentially" compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.
- In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets).
- Stone's celebrated "representation theorem for Boolean algebras" states that "every" Boolean algebra "A" is isomorphic to the Boolean algebra of all clopen sets in some (compact totally disconnected Hausdorff) topological space.
- A topological space [...] is perfect if all its points are limit points or, equivalently, if it coincides with its derived set [...].
- Another, more abstract, notion of continuity is continuity of functions between topological spaces in which there generally is no formal notion of distance, as there is in the case of metric spaces.
© dict.cc English-German dictionary 2024
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