Title of Paper :Phantom elements and its Applications

Author(s) : Jianzhong Pan and Moo Ha Woo

AMS Classification numbers :55P10,55P60,55P62,55R10

Addresses of Authors:


Jianzhong Pan
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

and 

Moo Ha Woo
Department of Mathematics Education , Korea University ,
 Seoul , Korea





Text of Abstract (try for 20 lines or less): 
In our previous work, 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.