Algebraic Topology · Problem 3F.2

Cohomology — Allen Hatcher

Mathematics — Topology · mittag-leffler-lim1-vanishing

Problem

Show that

\varprojlim^1 G_i = 0

if the sequence

\cdots \longrightarrow G_2 \xrightarrow{\alpha_2} G_1 \xrightarrow{\alpha_1} G_0

satisfies the Mittag--Leffler condition that for each

i

the images of the maps

G_{i+n} \to G_i

are independent of

n

for sufficiently large

n