Applications of the Stone-Čech compactification to free topological groups
Applications of the Stone-Čech compactification to free topological groups
In this note the Stone-Čech compactification is used to produce short proofs of two theorems on the structure of free topological groups. The first is: <italic>The free topological group on any Tychonoff space</italic> <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> <italic>contains, as a closed …