Is this in terms a of ruling?
It was primarily the "Open Door Policy" that opened relations between china and the united states, since this made it possible for many western countries to engage in trade with China.
Yes, it is true that in general the Northeast was the region most opposed to the annexation of Texas, since this would have meant an expansion of Southern power, which many in the Northeast wanted to avoid.
The Eastern Roman Empire, or Byzantium, managed to survive much longer then the Western Roman Empire because of multiple factors.
Some of the most important factors are that Byzantium had a strong leadership. The hierarchy was well placed, and the policies of the empire were good and prosperous.
Also, Byzantium was very wealthy, controlled important trade roots, had very well developed agriculture, and produced lot of goods, thus making the empire economically strong.
The military was well payed, well equipped, well organized, and it was loyal to the crown.
If you would have lived in Greece in about 300BC, you could have witnessed The battle of Thermopyle