On µ-separated sets and density of sets in uniform space

Abstract

Let  (x,u)  be  a  uniform space  and  u  be  an outer measure on  the  power  of the set  x  satisfying certain axioms.  We  introduced  the definitions  of  u-separated  sets and  density  of sets  with respect  to  the  measure u.  We  have shown  that  almost  all  the  results  on  u-separated sets  and  density  of  sets  in  R*  or metric  space  or topological  group  can  be  extended  in  uniform  space.