Automorphism groups of locally compact connected double loops are locally compact (Q689836)

It is a well known fact that the group \(\Sigma\) of all continuous collineations of a compact projective plane is a locally compact transformation group with respect to the compact-open topology [see \textit{H. Salzmann}, Pac. J. Math. 60, 217-234 (1975; Zbl 0323.50009) or \textit{Th. Grundhöfer}, Geom. Dedicata 21, 291-298 (1986; Zbl 0601.51020)]. This implies that the automorphism group \(\Gamma\) of a locally compact connected ternary field is locally compact, since such a ternary field coordinatizes some compact projective plane. In this paper this is generalized to the double loop case, i.e. it is proved that the automorphism group of a locally compact connected double loop is a locally compact transformation group with respect to the compact-open topology.