Stratifiable spaces as subspaces and continuous images of 𝑀₁-spaces

Abstract

It is shown that every stratifiable space is the image of an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{M_1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space under a perfect retraction.