# is surface always locally connected area in euklidian 3d?

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 this two not connected pieces of road in a term "surface".

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

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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