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Assume that $2^{\omega_1}=2^\omega=\mathfrak{c}$. Let $D$={ 0,1 }, and let $Y=D^\mathfrak{c}$. For $y\in Y\;$ let $\operatorname{supp}(y)$={$\xi<\mathfrak{c}:y(\xi)=1$}, the support of $y$, and let $X={x\in X$={$x\in Y:0<|\operatorname{supp}(x)|\le\omega_1}$; <|\operatorname{supp}(x)|\le\omega_1$}; $|X|=\mathfrak{c}^{\omega_1}=(2^{\omega_1})^{\omega_1}=\mathfrak{c}$. Does X have any $G_\delta$ diagonalproperties? |
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Assume that $2^{\omega_1}=2^\omega=\mathfrak{c}$. Let $D={ D$={ 0,1 }$, , and let $Y=D^\mathfrak{c}$. For $y\in Y\;$ let $\operatorname{supp}(y)={\xi<\mathfrak{c}:y(\xi)=1}$, \operatorname{supp}(y)$={$\xi<\mathfrak{c}:y(\xi)=1$}, the support of $y$, and let $X={x\in Y:0<|\operatorname{supp}(x)|\le\omega_1}$; $|X|=\mathfrak{c}^{\omega_1}=(2^{\omega_1})^{\omega_1}=\mathfrak{c}$. Does X have any diagonal properties? |
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Does X have any diagonal properties?Assume that $2^{\omega_1}=2^\omega=\mathfrak{c}$. Let $D={ 0,1 }$, and let $Y=D^\mathfrak{c}$. For $y\in Y\;$ let $\operatorname{supp}(y)={\xi<\mathfrak{c}:y(\xi)=1}$, the support of $y$, and let $X={x\in Y:0<|\operatorname{supp}(x)|\le\omega_1}$; $|X|=\mathfrak{c}^{\omega_1}=(2^{\omega_1})^{\omega_1}=\mathfrak{c}$. Does X have any diagonal properties?
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