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 $\subseteq$).

 

[pmacias]

The symbol \Subset is typically used in mathematics to represent the concept of one set being a subset of another set. In other words, all elements of the first set are also elements of the second set. This symbol is often used in set theory, which is a branch of mathematics that deals with the properties and relationships of sets. It is also commonly used in logic and computer science to represent containment or inclusion of one set within another. I hope this helps clarify the meaning of the \Subset symbol for you.