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August 9, 2011 / porton

Oblique products, related theorems and conjectures

I updated Funcoids and Reloids article. Now it contains a section on oblique products.

It now contains also the following conjectures:

Conjecture \mathcal{A} \times^{\mathsf{RLD}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} for some f.o. \mathcal{A}, \mathcal{B}.

Conjecture \mathcal{A} \times^{\mathsf{RLD}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} \subset \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B} for some f.o. \mathcal{A}, \mathcal{B}. Particularly, is this formula true for \mathcal{A} = \mathcal{B} = \Delta \cap \uparrow^{\mathbb{R}} \left( 0 ; +\infty \right)?

Conjecture \left( \mathcal{A} \ltimes \mathcal{B} \right) \cup \left( \mathcal{A} \rtimes \mathcal{B} \right) = \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B} for every f.o. \mathcal{A}, \mathcal{B}.

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