But the primitive, modal sound of shape-note singing, with its haunting open intervals, gave way to conventional notation and modern harmony.
22.
The space of all countable ordinals with the topology generated by " open intervals ", is a locally compact Hausdorff space.
23.
That is, if corresponds to a small open interval, there is no open with due to the appearance of the sets.
24.
These are used to delimit an open-open interval in mathematics, that is one which excludes both the start and end points.
25.
A "'strongly Darboux function "'is one for which the image of every ( non-empty ) open interval is the whole real line.
26.
You're right; you can't cover that interval with a countable collection of disjoint open intervals whose lengths sum to less than 1.
27.
Harbison's pungent harmonies and fitful writing for high voices, comforted by sustained open intervals in the lower voices, make that suffering manifest.
28.
The subbase consisting of all semi-infinite open intervals of the form alone, where is a real number, does not generate the usual topology.
29.
The second subbase generates the usual topology as well, since the open intervals with, rational, are a basis for the usual Euclidean topology.
30.
For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension " n " = 1.
