What is the Meaning of \Subset Symbol?

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SUMMARY

The \Subset symbol is commonly used in functional analysis to indicate that one set is compactly contained within another set. It serves as an alternative to the more complex \subset\subset notation. In practical applications, users can often substitute \Subset with the standard subset symbols \subset or \subseteq without losing meaning. This clarification is particularly relevant for those studying the Stationary Phase Method, as referenced in the provided mathematical literature.

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  • Understanding of set theory and notation
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  • Knowledge of the Stationary Phase Method
  • Basic mathematical symbol recognition
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  • Research the implications of compact sets in functional analysis
  • Study the differences between \subset, \subseteq, and \Subset in mathematical contexts
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Mathematicians, students of functional analysis, and anyone studying advanced mathematical concepts related to set theory and the Stationary Phase Method.

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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