Definition talk:Lower Semicontinuous

It's late, and I could be seeing things wrong, but shouldn't it be

$\ds \liminf_{x \mathop \to \bar x} \map f x \le \map f {\bar x}$? --Linus44 (talk) 01:10, 16 March 2013 (UTC)

Checking by googling, I think you're right. The author stopped by a couple of years ago to bang up a few pages but complained that his pages got changed to reflect the house-conventional notation that had evolved. He pointed out that this website did not obey the rules and that it needed to be shut down. Haven't seen him around for a while, so we may not get resolution on this. --prime mover (talk) 06:22, 16 March 2013 (UTC)

It seems from the proof here that

$\ds \liminf_{x \mathop \to \bar x} \map f x = \map f {\bar x}$

was intentional, not a typo. If the proof on that page holds water then I'm not sure what's going on. --Linus44 (talk) 13:36, 16 March 2013 (UTC)

Ignore it. Move on. --prime mover (talk) 13:40, 16 March 2013 (UTC)