On Continuity and Smoothness of Group Actions
نویسندگان
چکیده
by joint continuity of 7r at (go, x). If M is not metric the conclusion of Theorem 1 is no longer valid (consider G the circle and M the continuous functions on G with the topology of pointwise convergence). As a corollary, it is not hard to deduce that a Baire separable metric group G for which multiplication is continuous is a topological group (compare [9] and [2, p. 258]). For example the Ck or H" or CHa diffeomorphism group of a compact manifold satisfies these conditions; c.£. [5 l.
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