The remainder of the book proceeds from this theme, discussing equicontinuity, the strong topology
, operators, completeness, inductive limits, compactness, and barrelled spaces.
There is a natural topology, called the strong topology, on each PN space.
The strong topology on a PN space (V, v, [tau], [[tau].
The PN space under the strong topology is a Hausdorff space and satisfies the first countability axiom.
In this case, we will call this mapping an LS mapping, means the linearly homeomorphic with respect to the strong topology, in order to distinguish the notion of the linearly homeomorphic in topological vector space in which the linear structure and the topological structure are compatible with each other.
the strong topology on this PN space is the discrete topology on the set R.
theta]](N'), equipped with the strong topology, is called the space of distributions on N'.
PHI] (n times) and the convergence is in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (N') with respect to the strong topology.