Let $T$ be the one-point compattification, $E$ a real vector bundle, $\epsilon$ the trivial line bundle and $\Sigma$ the suspension operation. How can I prove that $$ T(\epsilon \oplus E) \simeq \Sigma T E\,\,\,\, ?$$
2026-03-26 01:27:29.1774488449
Identity in Thom spaces.
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Try and prove:
1) The Thom space of the trivial line bundle is $S^1$
2) For 'nice' spaces the one point compactification satisfies $(X \times Y)_+ = X_+ \wedge Y_+$