Background of several open problems I stumbled upon
This lists some problem aroused while I wrote my book “Algebraic General Topology. Volume 1”.
The draft of the book is now \hrefhttp://www.mathematics21.org/algebraicgeneraltopology.htmlavailable online.
Please first read the book and then collaborate with me in solving the below listed problems.
Theorems to prove:

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Intersection^{} with a staroid product^{} through its upper sets.
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 •
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More related materials:

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Direct products^{} in a category^{} of funcoids.

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Compact^{} funcoids.

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Metasingular numbers.
See the right sidebar of this page (”Attached articles”) for the list of problems.
TODO: More information should be put to this page.
See also \hrefhttp://researchtrends.wikia.com/wiki/Cartesian_closed_categories_containing_Top_and_Prox_as_subcategoriesthis page. Depsite of the fact that this page is written by me, I can’t remember whether that page notation is compatible with the notation in my book. Please analyse it and make its copy on PlanetMath.
Title  Background of several open problems I stumbled upon 

Canonical name  BackgroundOfSeveralOpenProblemsIStumbledUpon 
Date of creation  20130421 12:18:16 
Last modified on  20130421 12:18:16 
Owner  porton (9363) 
Last modified by  porton (9363) 
Numerical id  14 
Author  porton (9363) 
Entry type  Topic 
Classification  msc 54J05 
Classification  msc 54A05 
Classification  msc 54D99 
Classification  msc 54E05 
Classification  msc 54E17 
Classification  msc 54E99 