Ininfitely generated objects(fundamental groups of wild spaces)

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The central theme is the non-commutative Specker phenomenon, which is generic for uncountable groups. We studied it related to group theory and algebraic topology.In particular we proved the following. The fundamental groups of Peano continua determine the homotopy types and each homomorphism between thosegroupsis essentially induced from a continuous map. In general the fundamental group of an arbirary Peano continuum cannot be decomposed into a non-trivial free product at wild parts. There exists a 2-dimensional, cell-like, simply-connected, non-contractible Peano continuum.