Author Archives: dominiczypen

About dominiczypen

I'm interested in general topology, order theory, and graph theory. This link takes you to my preprints on arXiv.

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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