Abstract In this paper, we firstly analyse the position relation on four points from cases, that is, (i) both x and y are outside side of m n , (ii) either or is inner (iii) (iv) same . Then acquire eight kinds transitivity-like postulates cases. What more, discuss interrelationships between get some important deductibility theorems. Finally, give a few counter-examples to show inverse theorems...

There are millions of chess players around the world that play chess on websites like chess.com.1 According to chess.com,1 there are 600 Million chess-players worldwide, and more than 20 Million members on chess.com1 that play up to 1 Million games per day, and there are 360.000 tournament players and 1594 grandmasters of which only 2.2% are female, while it is free to play for everyone.1 Today...