NotTaR of Television Sets : Why is the convergence on my set bad nea..  
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Why is the convergence on my set bad near the edges

Very simple - nothing is quite perfect. Perfect convergence is not even necessarily possible in theory with the set of adjustments available on a typical TV. It is all a matter of compromises. Consider what you are trying to do: get three electron beams which originate from different electron guns to meet at a single point within a fraction of a mm everywhere on the screen. This while the beams are scanning at an effective writing rate of 20,000 mph across the face of a 27" CRT in a variable magnetic environment manufactured at a price you can afford without a second mortgage!