Bounded sets are a natural way to define a polar of a bounded set is an absolutely convex and absorbing set.
12.
Under the weak topology the bounded sets coincide with the relatively compact sets which leads to the important Bourbaki Alaoglu theorem.
13.
Near the ends of a bounded set, there would necessarily be a bliss point where local nonsatiation doesn't hold.
14.
This formulation allows one to define bounded operators between general topological vector spaces as an operator which takes bounded sets to bounded sets.
15.
This formulation allows one to define bounded operators between general topological vector spaces as an operator which takes bounded sets to bounded sets.
16.
It is usually taken to be an equicontinuous, uniformly bounded set of functions, which is compact by the Arzel? Ascoli theorem.
17.
For example, the left or right order topology on a bounded set provides an example of a compact space that is not Hausdorff.
18.
The continued fractions on the right hand side will converge uniformly on any closed and bounded set that contains no poles of this function.
19.
The Heine Borel theorem, as the result is now known, is another special property possessed by closed and bounded sets of real numbers.
20.
Bounded intervals are bounded sets, in the sense that their diameter ( which is equal to the absolute difference between the endpoints ) is finite.
