Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 $G_\delta$ diagonal?

share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

For a space $X$ to have a $G_\delta$ diagonal, it needs (although this is not enough) to have countable pseudo-character (i.e. every point must be a $G_\delta$). This is clearly not the case for your space.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.