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Topologies on the generalized plane. (English) Zbl 1325.30050

The author is dealing with the so-called generalized plane \(\Delta\) introduced by R. Arens and I. M. Singer [Trans. Am. Math. Soc. 81, 379–393 (1956; Zbl 0078.10902)] (see also [S. A. Grigoryan, Russ. Math. Surv. 49, No. 2, 1–40 (1994; Zbl 1108.30319); translation from Usp. Mat. Nauk 49, No. 2(296), 3–42 (1994)]). He compares the intrinsic topologies on the preimage of a finite-sheeted covering of \(\Delta\setminus K\), where \(K\) is a thin set, and shows that path-connected components coincide in these topologies.

MSC:

30G99 Generalized function theory
22D05 General properties and structure of locally compact groups
22D35 Duality theorems for locally compact groups
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