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A completely regular semimetric space M is con- structed which has no a-discrete network. The space M constructed has the property that every subset of M of cardinality 2Ao contains a limit point of itself; thus, assuming 2Ro =R, M is Lindelof. It is also shown from the same space M that, assuming 2Ro = Ni, there exists a regular Lindel6f semimetric space X such that XXX is not normal (hence not Lindel6f).

A regular Lindelöf semimetric space which has no countable network