The group of strong symplectic homeomorphisms in the L^∞-metric

The group SSympeo(M, ω) of strong symplectic homeomorphisms or group of ssympeomorphisms of a closed connected symplectic manifold (M, ω) was defined and studied in [2], [3]. In these papers the author uses the L^(1,∞)-metric on the group Iso(M, ω) of all symplectic isotopies. In this paper we study the set SSympeo(M, ω)^∞ of ssympeomorphisms in the L^∞-metric. We prove the equality between SSympeo(M, ω) and SSympeo(M, ω)^∞. This generalizes Müller's result [6] asserting that Hameo(M, ω) = Hameo(M, ω)^∞.