Der induktive Limes von abzählbar vielen FH-Räumen. Vereinigungsverfahren

The paper deals with the inductive limit of a countable set of FH-spaces (IFH-spaces). In contrast to completeness or metrizability there are properties such as the uniqueness of the topology of IFH-spaces which are preserved by the change from FH-spaces to IFH-spaces. In the special case of IFK-spaces the set of bounded sequences with weakly sectional convergence is considered. In particular, the convergence domain of the union of matrix transformations is an IFK-space. Analogous to the case of matrix transformations it is possible to prove theorems of the Mazur-Orlicz-type and theorems on perfectness and consistency.