How does one graph indifference curves for a set of Lexicographic preferences?

Question

Two Questions:

1. Since Lexicographic preferences are not continuous, is it still appropriate to use $\Bbb{R}^n_+$ to define my coordinate axes when drawing Lexicographic preferences? If not, what should I use instead?
2. Since the indifference sets for Lexicographic preferences are singletons, how do I draw them? What's the convention? Will a single point do?

(related to this question)

Answer 1

1. You can draw discontinuous functions in a standard $R^2$ space. For example when you draw a floor functions (a discontinuous function), the standard coordinates are still appropriate. Just make clear what to what part the discontinuous point belongs to. Usually, for lex. preferences, one draws only the preferred set. Here you can find a graph of this kind (page 2).

2. Yes, each point is an "indifferent singleton" (if we may say so, as your set has only one element, and of course you're indifferent between the same thing). The infinity number of points is not a problem. When you draw a preference map (for standard preferences), there are an infinite number of possible indifference curves. The idea is just to know how many you need to make your point. If you're using a software, you can plot with colors instead of a huge number of lines...