Vol. 56, No. 1, 1975

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Connector theory

Hidegoro Nakano and Kazumi Nakano

Vol. 56 (1975), No. 1, 195–213

Connector theory is a generalization of topology and uniformity. Each reflexive binary relation U of a space S induces a mapping from S to 2s wherein x S xU = {y : (x,y) U}∈ 2s. This mapping is called a connector. A uniformity on S is a set of connectors which meets certain conditions. The results in this paper include a necessary-sufficient condition for a connector-set to induce a unique topology, generalizations of continuous mappings and uniformly continuous mappings and characterizations of the connector-sets which correspond to a specific type of topology, for instance, a compact topology, a pseudo-compact topology.

Mathematical Subject Classification 2000
Primary: 54E15
Secondary: 54A05
Received: 1 August 1973
Published: 1 January 1975
Hidegoro Nakano
Kazumi Nakano