Embedding irreducible connected sets

Abstract: We show that every connected set

X

which is irreducible between two points

a

and

b

embeds into the Hilbert cube in a way that

X c u p c

is irreducible between

a

and

b

for every point

c

in the closure of

X

. Also, a connected set

X

is indecomposable if and only if for every compactum

Y s u p s e t e q X

and

a i n X

there are two points

b

and

c

in the closure of

X

such that

X c u p b, c

is irreducible between every two points from

a, b, c

. Following the proofs of these theorems, we illustrate a cube embedding of the main example from "On indecomposability of

". We prove the example embeds into the plane.

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