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Topic:
About generalizations
Replies:
21
Last Post:
Aug 20, 2013 11:45 PM




About generalizations
Posted:
Aug 13, 2013 4:22 PM


Is it a commonplace in mathematics when first a theorem is proved, and then one finds its most general generalization while preserve the same proof idea (without any creativity)?
Actually, I have written such a book. See http://www.mathematics21.org/algebraicgeneraltopology.html for its preprint.
The most important notion in this book are "funcoids".
Then in the chapter 14 I consider "pointfree funcoids", a trivial generalization of funcoids. I do exactly this thing (trivial generalization) about many theorems about funcoids transforming them into theorems about pointfree funcoids.
In this book I also do similar thing with generalization "filters on sets" > "filters on posets" > "filtrators".
In every of these generalizations I leave unchanged the same the conclusion of the theorem, changing only the conditions.
Having said all that, I slightly feel that I haven't presented it in the best possible way.
I want to hear some comments on this, not sure what exactly the nature of comments I want to hear.
 Victor Porton  http://portonvictor.org



