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Set of connected components of a filter (Solved)

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: filter
funcoid
reloid
Recomm. for undergrads: no
Posted by: porton
on: August 9th, 2007
Solved by: Porton, Victor
Conjecture   The set of connected components (regarding a funcoid or a reloid) is a partition of a filter.

See Algebraic General Topology for definitions of used concepts.

This conjecture has a trivial counterexample:

Consider endomorphism $ f=(\varnothing;A;A) $ of the category of funcoids where $ A $ is some infinite set. Then connected components regarding $ f $ are exactly ultrafilters on $ A $. The set of ultrafilters on an infinite set is not its partition.

Bibliography

*Victor Porton. Algebraic General Topology


* indicates original appearance(s) of problem.
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Please improve presentation!

On September 2nd, 2007 rs says:

Please, provide

1) definitions of the used concepts (to make the statement self-contained)

2) motivation (why this is important, examples, ...)

At the present state, this text is unfortunately not very useful for someone not acquainted with your manuscripts.

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