set & domain

logistic_guy said:
Sketch.

\(\displaystyle |z - 2 + i| \leq 1\)

Is this set a domain?

🤔
Click to expand...
The answer to this question strictly depends on which course it comes from, more especially the textbook is used.
It appears that this is a question about complex variables.
If you have access to a reasonably good library, look for Introduction To Complex Variables by F, P. Greenleaf.
That textbook defines a domain as a connected open set in the plane.
The set \(\displaystyle \{z\in\mathbb{C}:|z-2+i|\le 1\}\) being the set of points( a disk) centered at \(\displaystyle 2-i\) with radius \(\displaystyle \le 1\) is clearly connected but also it is closed.
 
pka said:
The answer to this question strictly depends on which course it comes from, more especially the textbook is used.
It appears that this is a question about complex variables.
If you have access to a reasonably good library, look for Introduction To Complex Variables by F, P. Greenleaf.
That textbook defines a domain as a connected open set in the plane.
The set \(\displaystyle \{z\in\mathbb{C}:|z-2+i|\le 1\}\) being the set of points( a disk) centered at \(\displaystyle 2-i\) with radius \(\displaystyle \le 1\) is clearly connected but also it is closed.
Click to expand...
Does this mean that a set that contains all of its accumulation points is never a domain? Since it is closed!
 
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