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Let a continuum , a compact space and a function
be given. Put
The function is said to be *lower (upper)* *semi-continuous*
provided that is open (closed) for each open (closed) subset
. It is said to be *continuous* provided that it is both
lower
and upper semi-continuous. This notion of continuity agrees with the one for
mappings between metric spaces.

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*Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih*

*2001-11-30*