Abstract: In this talk, we discuss some basic notions in algebraic topology such as singular (co)homology, categories and functors. We also describe some fundamental results about the strong (co)homology groups, derived limits of various inverse systems, and phantom maps. Moreover, we construct the same $n$-type structure for the suspension of the infinite complex projective space, and introduce the same $n$-type problems in homotopy theory.
This talk will be accessible to graduate students.