Example of Baire Space

Question

Can anybody supply an example of a Baire Space, that is neither locally compact nor metrizable. I would be gratefull also for some references.

Answer 1

As a trivial example, let $X,Y$ be Baire spaces with $X$ not locally compact and $Y$ not metrizable, and consider the disjoint union of $X,Y$.

Answer 2

The Sorgenfrey line is one example. It is not locally compact nor is it metrizable. Here is a paper showing that it is a Baire space..