A Setting for a Theorem of Bott

Inspired by Theorem A of Raoul Bott, Morse and Cairns have stated Corollary 23.3 below, a theorem of essentially the same character as Theorem A of Bott. The symbol ≃ in Corollary 23.3 means that the sets to the left and right of ≃ have the same homotopy type in the sense of Hilton (ref. 3, p. 3). Corollary 23.3 gives a setting to Bott's theorem in the theory of ``bowls'' introduced by Morse. The object of this note is to clarify and reinterpret the analysis presented as proof of Corollary 23.3 in reference 2.