Category Archives: Uncategorized

Basics on towers on the natural numbers

For we write if is finite, and we write if and . A tower is a collection of co-infinite subsets of such that for all we have and either or . ( is co-infinite if is infinite.) If are towers, … Continue reading

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A definition of minor (in graph theory)

Many people I talk to about graph theory feel some uneasiness when it comes to the notion of “minor”. I want to try to alleviate this feeling by providing the definiton of minor that I work with. First an easy … Continue reading

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Any graph or its complement is connected

This is a short note of something that I wasn’t sure whether it is true for infinite graphs. Let be any simple, undirected graph, finite or infinite, such that . By we denote the complement of . Proposition. At least … Continue reading

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Ode to ed (Unix standard text editor)

Encouraged by Eric S. Raymond’s book The Art of Unix Programming I have started using ed. My affection for it keeps growing. To begin with, it is the prime example of minimality, a property that is cherished all over the … Continue reading

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Coloring connected Hausdorff spaces

Motivation. I stumbled over the following hypergraph coloring concept when reading about an old (and open) problem by Erdos and Lovasz. Let be a hypergraph such that for all we have , and let be a set. Then a map … Continue reading

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Ihm ging ein Licht auf: Grieche entdeckte vor 2500 Jahren die Sonne

Ein Ereignis ist in diesen Sommertagen etwas in Vergessenheit geraten: Vor 2500 Jahren hat der Grieche Heliotides die Sonne entdeckt. Aus heutiger Sicht schwer zu glauben, dass diese Entdeckung eines grossen Kopfes bedurfte – aber schliesslich hatte es auch einen … Continue reading

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Homogeneous spaces generalized – and an open problem

Homogeneous spaces are topological spaces that locally look everywhere the same. Put in mathematical terms, is homogeneous if for any there is an isomorphism such that . We can generalize this by not restricting ourselves to a pair of points … Continue reading

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