J4 ›› 2013, Vol. 48 ›› Issue (2): 72-78.
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LUO Qing-jun1,2
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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 firstcountable 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
LUO Qing-jun1,2. Uniform topological spaces on R0 algebras[J].J4, 2013, 48(2): 72-78.
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http://lxbwk.njournal.sdu.edu.cn/EN/Y2013/V48/I2/72
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