difference between option prices of same maturity

[ajsa]

Hi David,

Could you take a look of following questions?
1) Is it true that the difference between American calls of same maturity cannot exceed the difference in their strike prices. what about European call?

2) Is it true that the price difference between two American puts of same maturity cannot exceed the difference in their strike prices. what about European put?

3) I wonder if euorpean put will increase with T regardless dividend.

Thanks.