Clone properties of topological spaces

V. Trnkova

Address. Mathematical Institute of Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic

E-mail: TRNKOVA@karlin.mff.cuni.cz

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.