MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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|cite|improve this question
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|cite|improve this answer

Your Answer


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.