I read this definition in a book about variational inequalities of Kinderlehrer and Stampacchia. The concept of weak continuity is mentioned in the definition, but I don't think it is related to the usual weak topology defined here. Thank you very much for any hints.

Citing " Example 6.5. There exists a real-valued function defined on the plane that is discontinuous and yet such that both partial derivatives exist and are continuous. Proof It is well know that if $f:\mathbb{R} \to \mathbb{R}$ is differentiable, then $f$ is continuous. What if $g:\mathbb{R}^...

It seems that perfect-squares and square-numbers are about the same thing, so creating a synonym perfect-squares $\to$ square-numbers seems reasonable to me. In fact, there already is tag synonym suggestion (by barto). There was a bit related discussion in this answer. (See revision history - ma...