• 자연과학논문집
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• 제10권1호
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• pp.9-12
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• 1998

본 논문에서는 $\psi : E \to F$가 섬유 화이버 함수일 때 후합성 $\psi :C_B(Y, E) \to C_B(Y, F)$도 섬유 화이버 함수이고, (X, A)가 닫힌 섬유 화이버 함수일 때 전합성 $\upsilon : C_B(X, E) \to C_B(A, E)$ 도 섬유 화이버 함수임을 보인다.

• 대한수학회보
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• 제36권4호
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• pp.671-682
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• 1999

Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.