Sentence examples for an isolated point from inspiring English sources

Let be an isolated point.

Let and let be an isolated point of.

Then λ is an isolated point of σ ( T ).

Then λ is an isolated point of σ(T) and α(T - λ) > 0. Since σ T * = σ T ¯, λ ̄ is an isolated point of σ(T*).

Proof Let λ be an isolated point of σ a ( d A B ∗ ).

Then 0 is an isolated point of σ(T) because σ(T + N) = σ(T).

In our case (Fig. 2), the vascular network has a dimension lying between 2 (plane surface) and 3 (volume), and any two-dimensional section of a vascular system (as in the case of a histological section) has a dimension lying between 0 (the dimension of a single isolated point) and 2 when the sectioned vessels entirely fill a plane surface (Figs. 3 and 4).

A bounded linear operator T ∈ B ( H ) is called a-isoloid if every isolated point of σ a ( T ) is an eigenvalue of T. Note that every a-isoloid operator is isoloid and the converse is not true in general.

Note that we consider a series of isolated point charges instead of a line of charge.

Theorem 2.3 Let T be a k-quasi-M-hyponormal operator, and let λ be a non-zero isolated point of σ ( T ).

In the first two examples, the extreme point ( 1, 1 ) is such that every neighborhood of ( 1, 1 ) contains both extreme as well as non-extreme points, whereas in the third case the extreme point ( 1, 1, 1 ) is an isolated extreme point.