  In this article some noncommutative topological objects such as NC mapping
cone and NC mapping cylinder are introduced. We will see that these objects are
equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we
introduce the notions of NC mapping cylindrical and conical telescope. Their
relations with NC mappings cone and cylinder are studied. Some results on their
K0 and K1 groups are obtained and the cyclic six term exact sequence theorem
for their k-groups are proved. Finally we explain their NCCW coplex structure
and the conditions in which these objects admit NCCW complex structures.

Quantum Algebra;Algebraic Topology