What are the limitations of Hilbert Curves?

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Is there a Hilbert curve for every space? as I understanding it in layman terms, it's a way to order a space sequentially which visits every place once.

Does it work with continuous spaces, or just discrete? Are there certain limitations of dimensionality that you cannot use a Hilbert curve to explore?

I guess I'm asking if everything can be serialized?

What must I understand to understand the boundary of the Hilbert Curve concept?