I think these would be useful and easy to implement.

    greater_close(a, b) = greater_equal(a, b) | isclose(a, b)
    less_close(a, b) = less_equal(a, b) | isclose(a, b)
    greater_no_close = greater(a, b) & ~isclose(a, b)
    less_no_close = less(a, b) & ~isclose(a, b)

The results are element-wise, just like the original functions.

I'm not sure if it is useful enough to be a part of numpy. If so, I will
try to implement them and make a pull request.
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