Plurisubharmonically separable complex manifolds

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Abstract: Let

M

be a complex manifold and

P S H^{c b} (M)

be the space of bounded continuous plurisubharmonic functions on

M

. In this paper we study when functions from

P S H^{c b} (M)

separate points. Our main results show that this property is equivalent to each of the following properties of

M

: (1) the core of

M

is empty. (2) for every

w_{0} i n M

there is a continuous plurisubharmonic function

u

with the logarithmic singularity at

w_{0}

. Moreover, the core of

M

is the disjoint union of 1-pseudoconcave in the sense of Rothstein sets

E_{j}

with the following Liouville property: every function from

P S H^{c b} (M)

is constant on each of

E_{j}

.

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