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A point p of a locally compact separable metric space L is a
local separating point of L provided there exists an open
set U of L containing p and two points x and y of the
component containing p of U such that
is the sum of two mutually separated point sets, one containing
x and the other containing y.
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-02-21