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Spaces not distinguishing convergences of real-valued functions. (English) Zbl 1067.54028
Summary: In [Topology Appl. 41, 25–40 (1991; Zbl 0768.54025)] we have introduced the notion of a wQN-space as a space in which for every sequence of continuous functions converging pointwisely to 0 there is a subsequence converging quasi-normally to 0. In the present paper we continue this investigation and generalize some concepts touched there. The content is a variety of notions and relationships among them. The result is another scale in the investigation of smallness and the question is how this scale fits with other known scales and whether all relations in it are proper.

MSC:
54G99 Peculiar topological spaces
54C30 Real-valued functions in general topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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