J4 ›› 2013, Vol. 48 ›› Issue (2): 72-78.

• Articles • Previous Articles     Next Articles

Uniform topological spaces on R0 algebras

LUO Qing-jun1,2   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
    2. College of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, Shaanxi, China
  • Received:2012-08-15 Online:2013-02-20 Published:2013-03-04

Abstract:

It is proved that the uniform topological space induced by a filter in an R0 algebra is a disconnected, zero-dimensional, locally compact, completely regular and firstcountable space, and a T0 space if and only if the filter is equal to {1}. Also, we proved that the negative operation, the join operation and the implication operation are continuous in the uniform topological space. Finally, some properties of the uniform topology are discussed on the quotient R0 algebra under the equivalence relation induced by a filter.

Key words: R0 algebra; filter MP; uniform topology

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