In this paper, some fundamental concepts are given relating to fuzzytopological spaces. Then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. Also the fuzzy topological spaces which are Hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group divisible designs and some association schemes with 5-classes is provided.

We say that an A 2-code is optimum if it has the minimum cheating probabilities and the minimum sizes of keys. We rst show that an optimum A 2-code implies an aane-resolvable design. Next, we de-ne an aane-resolvable + BIBD design and prove that an optimum A 2-code is equivalent to an aane-resolvable + BIBD design.