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

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Victor Porton

Posts: 621
Registered: 8/1/05
About generalizations
Posted: Aug 13, 2013 4:22 PM
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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
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 -

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