In our previous work[11] , a relation between Tsukiyama problem about self homotopy equivalence was found by using a generalization of phantom map. In this note , fundamental result is established for such a generalization. This is the first time one can deal with phantom maps to space not satisfying finite type condition. Application to Forgetful map is also discussed briefly.

In this paper we classify all free actions of finite groups on Calabi-Yau complete intersection of 4 quadrics in P, up to projective equivalence. We get some examples of smooth CalabiYau threefolds with large nonabelian fundamental groups. We also observe the relation between some of these examples and moduli of polarized abelian surfaces.

the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....

We introduce the concepts of intuitionistic fuzzy equality and intuitionistic fuzzy mapping. And we obtain some fundamental properties of intuitionisic fuzzy mapping. Furthermore, we give the decomposition of an intuitionistic fuzzy mapping by using intuitionistic fuzzy equivalence relation. 2010 AMS Classification: 03E72, 04A72

0. Introduction. A. Summary. A significant problem in topology is the classification of wild arcs in S3. The first fundamental paper in this area was written by Fox and Artin in 1948 [13]. There the authors developed rigorous algebraic means for demonstrating the nontameness of arcs. Some time later (1962) Fox and Harrold [14] succeeded in completely classifying a special class of wild arcs, th...

An automaton with concurrency relations A is a labeled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other. The concurrency relations induce a natural equivalence relation for nite computation sequences. We investigate two graph-theoretic representations of the equivalence classes of computat...