VECTOR SPACES WITH STRICTLY *-EQUABLE CONVERGENCE STRUCTURES

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ABSTRACT Certain results in connection with boundedness and precompactness, which are valid in topological vector spaces and locally bounded prelimit vector spaces, are extended to the class of strictly *-equable pre-limit vector spaces. This class contains the class of topological vector spaces. Hahn-Banach extension and separation theorems hold in the class of strictly *-equable prelimit vector spaces.