A strong shape theory with S-duality

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Fachbereich Mathematik, Johann-Wolfgang-Goethe Universität, Robert-Mayer Str. 6-10, 60054 Frankfurt a.M. 11, Germany

If in the classical S-category

a k P

, 1)

c o n t \in u o u s m a p π n g s a r e r e p l a c e d b y c o \mp a c t - o p e n s t r o n g s h a p e (= {\cos s}) m or ϕ s m s (c f . § 1 or [1], § 2), and 2) \land - \prod u c t s a r e \propto e r l y r e \int e r p r e t e d, t h e n a n S - d u a l i t y t h e or e m f or a r b i t r a r y \subset s

X ⊂ S^n!$! (rather than for compact polyhedra) holds (Theorem 2.1).

S-duality, Alexander duality, compact-open strong shape, virtual spaces

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