Address. Mathematical Institute of Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic
Abstract. Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.
AMSclassification. Primary: 54B10, 54C05, 54E40.
Keywords. Finite products, clone, first order language, rigidity, fix-point property, image-determining property, coconnectedness.