Every metric space can be given a metric topology, in which the basic open sets are open balls defined by the metric.
12.
All of this seems pretty silly; why can't you smoke in an open ball park, especially with the Marlboro Man in center field?
13.
When n > 1, open balls and open polydiscs are " not " biholomorphically equivalent, that is, there is no biholomorphic mapping between the two.
14.
Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.
15.
If \ R is viewed as a metric space, its open balls are the open bounded sets, and its closed balls are the closed bounded sets.
16.
"If ( Murphy's ) not there, it becomes an open ball game, " said Stan Caress, a political scientist at the State University of West Georgia.
17.
For the tournament this year, Wilson shipped more than 71, 000 US Open balls ( 12, 000 pounds worth ) to Flushing Meadows in New York City.
18.
Explicitly, a subset U of M is called "'neighborhood of the point x is any subset of M that contains an open ball about x as a subset.
19.
Let f be a holomorphic function on the open ball centered at zero and radius R in the complex plane, and assume that f is not a constant function.
20.
Although the usual base of open balls is not countable, one can restrict to the set of all open balls with rational radii and whose centers have rational coordinates.
