The Sorgenfrey line is not consonant

In Exercise 5.4.12 of the book, I ask the reader to prove that neither the space of rationals, Q, nor the Sorgenfrey line, R, is consonant. But the proofs I had in mind were much too simple-minded to stand any chance of succeeding, hence I classified this as important blooper #5 in the list of errata. Good news: Showing that R is not consonant is not that hard, finally. I will explain the argument in the full post. This will also be an excuse to explain some additional topological properties of R, an introduction to hereditary Lindelöfness (we will see that R is hereditarily Lindelöf, although it is not second-countable), and a few additional things in the appendices.

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