A standard example in elementary topology (e.g. Munkres) of a space which is limit-point compact (every infinite subset of the space has a limit point) but not compact is the minimal uncountable well-ordered set $S_\Omega$ in the order topology. One can easily show that the space is not compact, because it is not closed in its closure. But it is limit point compact, using the fact that the set has the least upper bound property. (If anyone wants the details I can write them out.)

Question is: Who first introduced this example?

I have checked without result in Counterexamples in Topology, and the history books available at my university, but I do not find any specific references. Munkres does not give a reference either. My googling proved equally unsuccessful, though I might not be searching for the right terms.

Any help would be appreciated!

A standard example in elementary topology (e.g. Munkres) of a space that is limit-point compact (every infinite subset of the space has a limit point) but not compact is the minimal uncountable well-ordered set $S_\Omega$ in the order topology. One can easily show that the space is not compact, because it is not closed in its closure. But it is limit point compact, using the fact that the set has the least upper bound property. (If anyone wants the details I can write them out.)

Question is: Who first introduced this example?

I have checked without result in Counterexamples in Topology, and the history books available at my university, but I do not find any specific references. Munkres does not give a reference either. My googling proved equally unsuccessful, though I might not be searching for the right terms.

Any help would be appreciated!