Vol. 105, No. 1, 1983

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Quasiregular nearness spaces and extensions of nearness-preserving maps

K. C. Chattopadhyay and Olav Njȧstad

Vol. 105 (1983), No. 1, 33–51

Every basic nearness (or quasi-nearness) induces a Čech closure operator. There is a 1-1 correspondence between the cluster generated Riesz nearnesses on a given T1 closure space and the principal (or strict) T1 extensions of the space. (In particular linkage compact extensions correspond to proximal nearnesses, F-linkage compact extensions correspond to contigual nearnesses, while ordinary compact extensions correspond to cluster generated weakly contigual nearnesses.

In this paper we discuss conditions under which a nearness-preserving map between nearness spaces can be extended to a continuous map between the corresponding principal extensions of the induced closure spaces. The concept of a quasi-regular nearness space plays an important role in this connection. The general results on extensions of nearness-preserving maps are used to obtain results on extension of continuous maps into regular linkage compact and F-linkage compact spaces.

Mathematical Subject Classification 2000
Primary: 54E17
Secondary: 54C20
Received: 8 May 1981
Revised: 9 March 1982
Published: 1 March 1983
K. C. Chattopadhyay
Olav Njȧstad