Re: Compact subsets of k-spaces (without separation axioms)

Gabor Lukacs writes:

I was wondering if anyone knows whether the first statement is true *without separation axioms*, i.e., whether for every topological space X, its k-ification kX and X have the same compact subspaces.

Sometime ago Alex Simpson advertised a paper "Comparing cartesian closed categories of (core) compactly generated spaces". http://www.cs.bham.ac.uk/~mhe/papers/ELS03.pdf where we have the same question (problem 9.2). Hence if anyone has an answer, please forward it to us as well - thanks. (I also take the opportunity to mention that we have updated the paper with some references given to us by some members of this list, in Section 3.) MHE