"neighbourhood" nach Englisch mit Beispielen - Kollokationen-Wörterbuch Englisch
- Let be the product of with itself, let be an open tubular neighbourhood of the diagonal in .
- It is defined to be the largest (closed) subset of X for which every open neighbourhood of every point of the set has positive measure.
- Now by computing derivatives at 0, the union contains an open neighbourhood of 1.
- A locally normal space is a topological space where every point has an open neighbourhood that is normal.
- However, if the function f is continuously differentiable in an open neighbourhood of a fixed point x, and , attraction is guaranteed.
- The basis of open neighbourhoods of 0 in R is given by the powers I, which are nested and form a descending filtration on R:
- If is open it is called an open neighbourhood.
- Here, a network is a family of sets, for which, for all points and open neighbourhoods , there is a for which .
- It is symmetric since which by continuity of the inverse is another open neighbourhood of the identity.
- It is transitive since where and are open neighbourhoods of the identity such that ; such pairs exist by the continuity of the group operation.
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