Abstract: By a branch we mean an irreducible germ of a complex plane curve. The intersection
multiplicity of two branches divided by their multiplicities satisfies the axioms of
logarithmic distance [9]. The properties of balls defined by using this distance are
analogous to that in ultrametric spaces. In this paper for an arbitrary fixed branch
we construct effectively a new branch such that the distance between branches is
an arbitrary rational greater than or equal to one. This crucial fact was proved
in [1]. This fact allows to show, for example, that equal balls have equal diameters.
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