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How can c be "way below" itself? -- karlheg 08:35, 2004 Nov 24 (UTC)
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)
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)
Given the complete lattice determined by the open sets of an arbitrary topological space ordered by set inclusion, the compact elements are not the compact sets of the space since in general compact sets are not open (and so would not even be members of this lattice). As far as I can tell, the name "compact" comes from the analogy with the topological definition, unless there is a restricted set of topological spaces for which this is true. Ron.garcia ( talk) 20:37, 8 May 2010 (UTC)
Please add sections:
Thanks, Hooman Mallahzadeh ( talk) 09:21, 8 February 2023 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
How can c be "way below" itself? -- karlheg 08:35, 2004 Nov 24 (UTC)
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)
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)
Given the complete lattice determined by the open sets of an arbitrary topological space ordered by set inclusion, the compact elements are not the compact sets of the space since in general compact sets are not open (and so would not even be members of this lattice). As far as I can tell, the name "compact" comes from the analogy with the topological definition, unless there is a restricted set of topological spaces for which this is true. Ron.garcia ( talk) 20:37, 8 May 2010 (UTC)
Please add sections:
Thanks, Hooman Mallahzadeh ( talk) 09:21, 8 February 2023 (UTC)