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For questions requesting examples of a certain structure or phenomenon

4 votes
Accepted

Semi-metrizable spaces with countable chain condition

There exists a counterexample, that is, a non-separable semi-metrizable space with ccc, which can be constructed as follows. Consider the countable power $\mathbb Z^\omega$ of the group of integers. F …
Taras Banakh's user avatar
  • 41.8k
5 votes
Accepted

How could I see quickly that this space is not normal?

Theorem. A dense subspace $X$ of the Tychonoff cube $[0,1]^\kappa$ is not normal if $X$ contains an uncountable closed discrete subspace $D$ such that each $x\in D$ has finite support $\mathrm{supp}(x …
Taras Banakh's user avatar
  • 41.8k
5 votes
Accepted

Let $X$ be a Lindelof, perfectly normal, $\sigma$-space. Must $X$ be separable?

If a $\sigma$-space $X$ is Lindelof, then it is paracompact and by Theorem 4.4 of Gruenhage's survey "Generalized Metric Spaces" in the "Hanbook of Set-Theoretic Topology", $X$ has countable network a …
Taras Banakh's user avatar
  • 41.8k
4 votes

Proofs without words

The picture below proves (without words) that it is possible to draw the classical Desargues configuration $D_{10}$ using points in the set $\{-3,-2,-1,0,1,2,3\}^2$. This picture was produced by Alex …