DIVISOR TOPOLOGIES AND THEIR ENUMERATION

‎For a positive integer m‎, ‎a subset of divisors of m is called a \textit{divisor topology on m} if it contains ۱ and m and it is closed under taking \gcd and \rm lcm‎. ‎If m=p_۱\dots p_n is a square free positive integer‎, ‎then a divisor topology m corresponds to a topology on the set [n]=\{۱,۲,\ldots,n\}‎. ‎Giving some facts about divisor topologies‎, ‎we give a recursive formula for the number of divisor topologies on a positive integer‎.

کلیدواژه ها:

Topology ، Divisor topology ، Semi-divisor topology