What is the Meaning of \Subset Symbol?

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The symbol \Subset is often used in mathematical contexts, particularly in functional analysis, to indicate that one set is compactly contained within another. It serves as an alternative to the more complex notation \subset\subset. While it may not be universally recognized in all mathematical texts, it can generally be interpreted similarly to the standard subset symbols \subset or \subseteq. The discussion highlights a specific source where the symbol is defined, emphasizing its relevance in the context of the Stationary Phase Method. Understanding this symbol can enhance clarity in mathematical discussions involving set containment.
Gabriel Maia
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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.
 
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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?
 
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http://www.math.purdue.edu/~sfholman/dHHU_Chap2.pdf First page, definition 2.1
 
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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).
 
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