What is the Meaning of \Subset Symbol?

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Discussion Overview

The discussion revolves around the meaning of the mathematical symbol \Subset, particularly in the context of the Stationary Phase Method. Participants seek clarification on its definition and usage in mathematical literature.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant expresses confusion about the \Subset symbol and requests help in understanding its meaning.
  • Another participant mentions they could not find the symbol in the source they were reading and asks for clarification on the original source of the symbol.
  • A third participant provides a link to a document where the symbol is defined, indicating its presence in that context.
  • A later reply suggests that \Subset is often used as an alternative to \subset\subset, indicating that it signifies one set being compactly contained within another. This participant notes that for practical purposes, \Subset can be mentally replaced with the usual subset symbols.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the symbol's meaning, as there are differing views on its usage and context, particularly regarding its application in functional analysis versus other areas of mathematics.

Contextual Notes

Some participants note that the symbol may not be universally recognized or defined in all mathematical texts, leading to potential confusion regarding its interpretation.

Who May Find This Useful

This discussion may be useful for individuals studying mathematical symbols, particularly in the context of set theory and functional analysis, as well as those exploring 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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