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    Nice representation of open sets in $\sigma$-algebras in certain circumstances
                Let $(X,\tau)$ be a topological space. For a given topological base  $\mathcal{E}$ for $\tau$, let us denote Bor$(\mathcal{E})$, by the smallest $\sigma$-algebra containing $\mathcal{E}$. 
Q.  Assume ...
            
        
       
    
            4
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            111
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    Nice arrangement of open sets in $\sigma$-algebras
                Let $X$ be a topological space and  $\mathcal{E}$ be a topological base for $X$. Let us denote Bor$(\mathcal{E})$, by the smallest $\sigma$-algebra containing $\mathcal{E}$. 
Q.  Let $O$ be an open ...