Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have some geometry in 3d (like road surface or terrain surface) and there could be several not connected parts of a road. So I'd like to know if I may unite these two not connected pieces of road in a term "surface".

And if I couldn't, then what is the best mathematical term for this?

share|cite|improve this question
If I'm interpreting your question correctly, you have two currently separate surfaces that share a boundary, and you want to join them into a single surface? – J. M. Oct 20 '10 at 14:24
Not exactly. I have two surfaces that do not share any boundary edge/point. Any i need to know how can i call this object. – Alex Stamper Oct 20 '10 at 15:17
Could it still be a surface, or for surface it is obligatory to have some boundaries between its parts? – Alex Stamper Oct 20 '10 at 15:18
From my perspective, a surface may be an object that has multiple components. So, I could talk about a surface that is two disjoint spheres, for example. However, it is important to clarify your terms. Since some people will assume a surface is connected, you should say that in your work the term encompasses objects that have multiple components. – yasmar Oct 20 '10 at 15:43
up vote 2 down vote accepted

The only requirement for a surface is that it be two dimensional. It can be connected or not connected. So it's OK mathematically to call your multi-component terrain object a "surface", even though in everyday language people might think of it as several surfaces.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.