david schrieb:

I'm using the article (koma-script) class and I need to change the
title-labeling as followed:

1 Section (ending with no dot)
1.1. Subsection (ending with dot)
1.1.1. Subsubsection (ending with dot)

What is the best solution for this problem?

You can only have dots at the end for all (sub)section numbers or no dots for all.
If you write in german there is the following rule
(see Duden, 1996, R3 and R4):

- always no dot behind the last number
- exception: when you use letters or roman numerals to number sections,
  you have to end all, also the normally numbered section numbers with a
  dot

To make it short, use the document option "pointlessnumbers" or "pointednumbers" when you have a koma-script document.

regards Uwe

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