Topological Lumpiness and Topological Extreme Amenability.

In this paper we give some characterizations of topological extremeamenability. also we answer a question raised by ling [5]. in particular we prove that if t is a borel subset of a locally compact semigroup s such that m(s)* has a multiplicative topological left invariant mean then t is topological left lumpy if and only if there is a multiplicative topological left invariant mean m on m(s)* such that m((chi)t)=1, where (chi)t is the characteristic functional of t. consequently if t is a topological left lumpy locally compact borel subsemigroup of a locally compact semigroup s, then t is extremely topological left amenable if and only ifs is.