Home » Subject » Topology
Importance: Low ✭
Author(s): Porton, Victor
Subject: Topology
Keywords: filter products
Recomm. for undergrads: no
Posted by: porton
on: August 9th, 2011
Conjecture   $ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} \subset \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} $ for some filter objects $ \mathcal{A} $, $ \mathcal{B} $. Particularly, is this formula true for $ \mathcal{A} = \mathcal{B} = \Delta \cap \uparrow^{\mathbb{R}} \left( 0 ; + \infty \right) $?

A weaker conjecture:

Conjecture   $ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} $ for some filter objects $ \mathcal{A} $, $ \mathcal{B} $.

See Algebraic General Topology for definitions of used concepts.

The first conjecture probably has no use by itself but proving it may be somehow challenging, just like Fermat Last Theorem.

Bibliography

*Victor Porton. Algebraic General Topology


* indicates original appearance(s) of problem.
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