Talk:Compact element

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[edit] Way below

How can c be "way below" itself? --karlheg 08:35, 2004 Nov 24 (UTC)

Inconceivable, right? Perhaps the word does not mean what you think it means....

We say that an element x is called "way below y" if x is an element of every ideal I satisfying sup(I) ≥ y.

Since the principal ideal generated by y satisfies this condition, we know that any x which is way below y must be in it, i.e., must satisfy x≤y -- but not necessarily x<y.

(So the short answer is: the word "below" has to be interpreted as "below-or-equal".)

Aleph4 11:41, 14 June 2006 (UTC)

In view of this definition, the term "way below" merely duplicates in obscure language the preceding condition, which is the definition of being "way below" itself. I removed it. Zaslav 09:46, 22 March 2007 (UTC)

[edit] Introduction

The introduction is incomprehensible. Someone should write a clear and simple intro that does not require previous knowledge. I will see if I can do it, but others are welcome to the job. Zaslav 09:24, 22 March 2007 (UTC)

[edit] Standard

I removed the following remark: "Compact elements are standard." It makes no sense. Is "standard" a technical term? Then it needs explanation; please, someone, do that. If not, then what does the sentence mean? Zaslav 09:40, 22 March 2007 (UTC)