Rigidity of the second symmetric product of the pseudo-arc

Let P denote the pseudo-arc and let F2(P)={{p,q}:p,q∈P} denote the second symmetric product of P. The main result in this paper is the following: if E:F2(P)→F2(P) is an embedding, then there is an embedding e:P→P such that E({p,q})={e(p),e(q)}. We obtain that the autohomeomorphisms of F2(P) are indu...

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Bibliographic Details
Published in:Topology and its applications 2017-04, Vol.221, p.440-448
Main Authors: Calderón, Irving, Hernández-Gutiérrez, Rodrigo, Illanes, Alejandro
Format: Article
Language:English
Subjects:
Degree of homogeneity
Embedding
Hyperspace
Induced map
Pseudo-arc
Rigidity
Symmetric product
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Summary:Let P denote the pseudo-arc and let F2(P)={{p,q}:p,q∈P} denote the second symmetric product of P. The main result in this paper is the following: if E:F2(P)→F2(P) is an embedding, then there is an embedding e:P→P such that E({p,q})={e(p),e(q)}. We obtain that the autohomeomorphisms of F2(P) are induced, P has rigid hyperspace F2(P), and the degree of homogeneity of F2(P) is exactly 3.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.02.023