What is the Meaning of \Subset Symbol?

[Gabriel Maia]

Hi. I was reading a chapter about Stationary Phase Method and I got stuck with this symbol $\Subset$. I looked it up on tables os mathematical symbols but could not find its meaning.

Can you help me?

Thank you.

 

[danjordan]

I was reading about that from here http://www.math.ku.dk/~gimperlein/dif11/dif11_kim_stationaryphase.pdf but saw no such symbol. What's your source?

 

[Gabriel Maia]

http://www.math.purdue.edu/~sfholman/dHHU_Chap2.pdf First page, definition 2.1

 

[Hypersphere]

This seems more like a math question to me (I've only seen it in functional analysis), but anyway. In this (and most cases), $\Subset$ tends to be used as an alternative to (the in my opinion rather ugly) $\subset\subset$, and means that one set is compactly contained (or embedded) in the other. For many intents and purposes, you can mentally replace $\Subset$ by the usual subset symbols ($\subset$ or $\subseteq$).