Locally connected space
= Locally connected space
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= Local connectedness
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A <topological space> has <local connectedness> when every point has a <neighborhood> basis of <connected> <open sets>. In particular, a planar <domain> has <local connectedness>, but its <domain boundary> need not be. <Local connectedness> of the <boundary> is the condition governing a continuous extension of a <conformal bijection> to the parametrizing circle.