A core-free semicovering of the Hawaiian Earring

The connected covering spaces of a connected and locally path-connected topological space X can be classified by the conjugacy classes of those subgroups of pi(1)(X, x) which contain an open normal subgroup of pi(1)(X, x), when endowed with the natural quotient topology of the compact-open topology on based loops. There are known examples of semicoverings (in the sense of Brazes) that correspond to open subgroups which do not contain an open normal subgroup. We present an example of a semicovering of the Hawaiian Earring liii with corresponding open subgroup of pi(1)(H) which does not contain any nontrivial normal subgroup of pi(1)(H). (C) 2013 Elsevier B.V. All rights reserved.