Alexandroff Square is a W-space

We present a non-metrizable compact space called Alexandroff Square, which is Example 101 in Steen and Seebach [4]. This is a compact space that is due to Alexandroff and Urysohn, which can be traced back to their paper published in 1929. One of the facts duscussed in [4] is that the Alexandroff Square is not first countable at any point on the diagonal. We show that the Alexandroff Square, though not first countable, is a W-space (a strong convergence property weaker than the first...