German for “contiguous simplicial maps”

Question

Is there an established German word for “contiguous” in the sense of contiguous simplicial maps?

Background

Definition. Two simplicial maps $f$ and $g$ from $\mathcal K$ to $\mathcal L$ are called contiguous, if whenever $S$ is the set of vertices of a simplex of $\mathcal K$ the set $f[S]\cup g[S]$ is the set of vertices of a simplex of $\mathcal L$.

I am teaching a class in German, and I will go with „benachbart“, if no-one knows a better word. I would look if the concept is used in Seifert and Threlfall, but I do not have it at hand.

I would use "angrenzend" which results from the German noun "Grenze" for border. It means that they share the same border. — Jan Rothkegel, Dec 21 '18 at 17:35
@FWE, those were most likely the lecture notes that I was preparing when I asked the question. Thanks, that made my day ;) — Carsten S, Mar 13 '19 at 19:28
Why don't you just look at https://en.wikipedia.org/wiki/Contiguity_(probability_theory) , then select "languages" ? — Gyro Gearloose, Mar 15 '25 at 18:21
@GyroGearloose, thank you, but while this is the right word it is not the right concept. — Carsten S, Mar 15 '25 at 18:41
"while this is the right word it is not the right concept." Your mind is open: you see the difference between words and concepts. Not all concepts do have a proper word-to-word translation from one language to another. — Gyro Gearloose, Mar 15 '25 at 18:49

score 2 · Answer 1 · answered Mar 13 '19 at 17:37

2

The German term "benachbart" seems appropriate - see e.g.

(1) 15.3 in Carsten Schultz' Seiten

(2) p. 31 in Eberhard Schock.Konvergente Iterationsverfahren für flach konvexe Banachräume

For the second I am not sure if the meaning is identical to yours though.

answered Mar 13 '19 at 17:37

FWE

1,915

As noted in the comments to the question, the first reference is not that helpful in this context, but the second one is, thanks. – Carsten S Mar 13 '19 at 19:32

Paul Frost · Answer 2 · 2025-03-16T10:32:38.837

An answer to a very old question ... You asked for Seifert and Threlfall's "Lehrbuch der Topologie". You can find it here and the English translation here.

Seifert and Threlfall primarily do not consider abstract simplicial complexes (given by the sets of vertices and simplices), but geometric simplicial complexes which are toplogical spaces with a simplicial decomposition into topological images of rectilinear simplexes. In modern terminology one would call this a triangulation of a polyhedron.

However, they introduce the "schema of a simplicial complex" which can be regarded as an abstract simplicial complex.

They also introduce simplicial maps and prove that each continuous map between simplicial complexes is homotopic to a simplicial map, provided that the simplicial decomposition of the domain is sufficiently fine. However, they do not define the concept of contiguous simplicial maps.

In the English translation the word "contiguous" occurs on p. 282 (contiguous $n$-cells; cells and cell complexes are introduced in Section 67). It translates the German "angrenzend" (see p. 271 of the German text).

This suggests that the German root of the English "contiguous" is "angrenzend".

In the context of your question this makes perfect sense: The images of any simplex in the domain under the maps $f, g$ are required to be faces of a simplex in the codomain and are angrenzend in that sense.

Anyway, I do not think that that using "benachbart" would be a bad choice in German. I do not know any German textbook dealing with contiguous maps (though my knowledge is limited), and this indicates that you would not violate any standard German terminology.

Thank you for taking the time to write this answer. While it is indeed because of the age of the question not of immediate practical value to me it may be to someone else. And for me it has nostalgic value. — Carsten S, Mar 15 '25 at 18:40

German for “contiguous simplicial maps”

2 Answers2