I am looking for good simple examples that capture the difference in definitions between semi-continuity and continuity from the left/right.
I am certainly able to construct examples and wikipedia also lists some:
http://en.wikipedia.org/wiki/Semi-continuity
But the given examples are semi-continuous by the trivial fact of having a maximum at the point in question.
Are there examples for functions that are upper semicontinuous, but not left/right continuous and for functions that are left continuous but not upper/lower semicontinuous that capture at the same time a larger part of the subtleties of the definitions and are given by simple expressions?