In [Math.\ Ann.\ 330, No.1, 151--183 (2004; Zbl 1064.46009), reviewed above], \textit{P.~Koszmider} solved (in ZFC) the hyperplane problem for \(C(K)\)-spaces in the negative. His approach was to construct compact spaces \(K\) for which all operators on \(C(K)\) are of a special type called weak multipliers. In fact, assuming the continuum hypothesis he was able to construct (even connected) compact spaces \(K\) for which every operator on \(C(K)\) is the sum of a multiplication operator and a weakly compact operator. In this paper, such a compact space is called a Koszmider space. The purpose of the present paper is to remove CH from the construction of Koszmider spaces. The author develops a topological property for \(K\) to be a Koszmider space, and he constructs connected Koszmider spaces purely in ZFC. These arise as representation spaces of certain lattices. The examples constructed here are, however, not separable as opposed to Koszmider's. The paper is very clearly written; but the reader should be cautioned that the author apparently refers to a preprint version of Koszmider's work. So weak multipliers are called centripetal operators here, and cross-referencing does not seem to match the published version.