Links between connections, parallel transports, and transports along   paths in differentiable fibre bundles
  The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "connection" and "(axiomatically defined) parallel transport" is established. Some results which are specific for topological and vector bundles are presented. 
Bozhidar Z. Iliev (Institute for Nuclear Research and Nuclear Energy,   Bulgarian Academy of Sciences, Sofia, Bulgaria)