Connectedness is closure-preserved
From Topospaces
This article gives the statement, and possibly proof, of a topological space property (i.e., connected space) satisfying a topological space metaproperty (i.e., closure-preserved property of topological spaces)
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Statement
Suppose is a topological space and
is a subset of
that is a connected space with the subspace topology from
. Then, the closure of
in
, denoted
, is also a connected space with the subspace topology from
.