lower boundary?

From: boyandshark (amitgandhi_at_gmail.com)
Date: 03/01/05 

Date: 1 Mar 2005 11:52:34 -0800

Does anyone know what the terms "lower boundary" and "upper boundary"
mean in the context of a compact, connected subset of R^2? I am trying
to translate what these terms mean from something I am reading.

Here is an example:

Consider the rectangle R=[0,2] x [0,4] in R^2. Let A= {(x,2)| 0<=x<=1 }
union [1,2]x[1,3], which is contained in R.

Then the lower boundary of A in R is given by L={(x,2) | 0<=x<=1 }
union {(1,y) | 1<=y<=2} union {(x,1) | 1<=x<=2}.

I get intuitively what it means in terms of this example, but does
anyone know a formal definition?

Thanks
amit

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