The Structure of the -ideal of -porous Sets

We show a general method of construction of non-porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non-porous Suslin subset of a topologically complete metric space contains a non-porous closed subset. We show also a suucient condition, which gives that a certain system of compact sets contains a non-porous element. Namely, if we denote the space of all compact subsets of a compact metric space E with the Hausdorr metric by K(E), then it is shown that each analytic subset of K(E) containing all countable compact subsets of E contains necessarily an element, which is non-porous subset of E. We show several applications of this result to problems from real and harmonic analysis (e.g. the existence of a closed non-porous set of uniqueness for trigonometric series). Finally we investigate also descriptive properties of the-ideal of compact-porous sets.