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.

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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Two notions of continuity in the space of natural sequences

In this presentation by Martín Escardó I came across a nice concept of continuity in the set of all functions . For and we say that if and only if for all we have . Then we define to be finitely … Continue reading

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A reformulation of Hadwiger’s conjecture

Let be a finite, simple, undirected graph. Hadwiger’s conjecture states that if then is a minor of . Let’s call that statement (Hadw). We show that it is equivalent to the following statement: (Hadw’): If is not a complete graph, … Continue reading

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Accumulation without converging subsequence

“Any sequence with an accumulation point also has a subsequence converging to that point” — right? I believed this until yesterday when I stumbled over the following curious, and countable, Hausdorff space. Endow with the following topology: is given the … Continue reading

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