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In my recent research, I defined a topological space $X$ to be $EZ$-space if for every open subset $A$ of $X$ there exists a collection ${A_{\alpha}: \{A_{\alpha}: \alpha\in S}$ S\}$of clopen subsets of$X$such that$cl_{X}{A}=cl_{X}({\bigcup_{\alpha\in S}A_{\alpha}})$. Also I defined$X$to be$EB$-space if if for every cozero-set$H$, of$COZ[X]$there exists a collection${H_{\alpha}: \{H_{\alpha}: \alpha\in S}$S\}$ of clopen subsets of $X$ such that $cl_{X}{H}=cl_{X}({\bigcup_{\alpha\in S}H_{\alpha}})$.

For example, any zerodimensinal space is an $EZ$-space. and any basically disconnected space is an $EB$-space.

Question: Give an example of a completely regular $EB$-space which is not $EZ$-space?

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# Example of a topological space.....

In my recent research, I defined a topological space $X$ to be $EZ$-space if for every open subset $A$ of $X$ there exists a collection ${A_{\alpha}: \alpha\in S}$ of clopen subsets of $X$ such that $cl_{X}{A}=cl_{X}({\bigcup_{\alpha\in S}A_{\alpha}})$.

Also I defined $X$ to be $EB$-space if if for every cozero-set $H$, of $COZ[X]$ there exists a collection ${H_{\alpha}: \alpha\in S}$ of clopen subsets of $X$ such that $cl_{X}{H}=cl_{X}({\bigcup_{\alpha\in S}H_{\alpha}})$.

For example, any zerodimensinal space is an $EZ$-space. and any basically disconnected space is an $EB$-space.

Question: Give an example of a completely regular $EB$-space which is not $EZ$-space?