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Zbl 0603.54033
Mršević, Mila
On pairwise $R\sb 0$ and pairwise $R\sb 1$ bitopological spaces.
(English)
[J] Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 30(78), 141-148 (1986). ISSN 0007-4691

In a bitopological space $(X,\tau\sp 1,\tau\sp 2)$ the binary relation $\sim$ is defined in the following way: $x\sim y\Leftrightarrow qcl\{x\}=qcl\{y\}$, where $qcl\{x\}=\tau\sp 1cl\{x\}\cap \tau\sp 2cl\{x\}$ is the quasiclosure of $\{$ $x\}$. If $\tilde X$ is the quotient space of X obtained by the equivalence relation $\sim$, many of the bitopological properties are shared by X and $\tilde X.$ Some new results concerning pairwise $R\sb 0$ and pairwise $R\sb 1$ bitopological spaces are obtained.
MSC 2000:
*54E55 Bitopologies
54B15 Quotient spaces, etc. (general topology)
54D10 Lower separation axioms

Keywords: quasiclosure; quotient space; pairwise $R\sb 1$ bitopological spaces

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