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The way in which Niggli characters are introduced nowadays is not very satisfying. In this paper a more exact abstract method based on topological concepts is proposed. Any lattice can be represented by a point in E5, its Niggli point. Then to any system of lattices there corresponds a set of points in E5 called the image of this system. A Bravais type is taken formally as a system of all lattices of this type. The same can be done with the Niggli characters. The main result is: The image of a Niggli character is a component (i.e. a maximum connected subset) of the image of that Bravais type which contains the character. The image of any Niggli character is a convex set. This enables a simple physical (dynamical) interpretation. Since the decomposition of a set in E5 into components is unique it can be used conversely for definition of the Niggli characters.
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