= Semilocally simply connected space
= Semilocally simply connected
{synonym}
A <topological space> is semilocally simply connected if every point has an open neighbourhood whose loops based at that point become <null-homotopic> in the whole space. The neighbourhood itself need not be <simply connected>. Together with <path connectedness> and <local path connectedness>, this condition gives the classical existence and classification of connected <covering spaces> by <subgroups> of the <fundamental group>.
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