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Mildly ( 1 , 2 ) * -normal spaces and some bitopological functions

K. Kayathri, O. Ravi, M. L. Thivagar, M. Joseph Israel (2010)

Mathematica Bohemica

The aim of the paper is to introduce and study a new class of spaces called mildly ( 1 , 2 ) * -normal spaces and a new class of functions called ( 1 , 2 ) * - rg -continuous, ( 1 , 2 ) * - R -map, almost ( 1 , 2 ) * -continuous function and almost ( 1 , 2 ) * - rg -closed function in bitopological spaces. Subsequently, the relationships between mildly ( 1 , 2 ) * -normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly ( 1 , 2 ) * -normal spaces, properties of the new bitopological functions and preservation theorems for...

On a class of real normed lattices

C. Alegre, Jesús Ferrer, Valentín Gregori (1998)

Czechoslovak Mathematical Journal

We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that E is a quasi-Baire space iff ( E , T ( 𝒰 ) , T ( 𝒰 - 1 ) ) , is a pairwise Baire bitopological space, where 𝒰 , is a quasi-uniformity that determines, in L . Nachbin’s sense, the topological ordered space E .

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