Is there a modern generally accepted answer regarding the notions of k-space or compactly generated space?
For example there are currently at least 3 formally distinct notions of k-space in wide circulation: 1) Kelley's `General Topology' 2) nlab 3) Wikipedia.
Definition 1) According to Kelley, X is a k-space means if S is not closed in X, then there exists a closed compact subspace C in X, such that the intersection of C and S is not closed in X. (The Kelley notion of k-space also appears in the paper `Between T-1 and T-2' by Wilansky).
Definition 2) According to n-lab, X is a k-space means if S is not closed in X, there exists a compact Hausdorff space K and a map f:K-->X such that the preimage of S is not compact. This is equivalent to X is CG ( compactly generated) in Neil Strickland's notes on CGWH spaces.
Definition 3) Currently 10/03/12, wikipedia has a 3rd notion of k-space and declares that X is a k-space or a CG space provided if S is not closed in X, then there exists a compact subspace C in X, such that the intersection of C and S is not compact.
Are any of definitions 1,2,3 equivalent if X is not weakly Hausdorff?