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In this paper we prove some results about the stable homotopy and cohomotopy of spaces related to the infinite real protective space RP ∞ . These include M. E. Mahowald's conjecture on the limit of stable homotopy of stunted real projective spaces RP 2 N + m /RP 2 N − m as N, m → ∞, G. Segal's Burnside ring conjecture for and the stable analogue of a conjecture of D. Sullivan on RP ∞ .
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Wen‐Hsiung Lin (1980) studied this question.
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