Geodesic
A Note on Fixed Point Sets and Wedges
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 453-455

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DOI

A space Z is said to have the complete invariance property (CIP) provided that every nonempty closed subset of Z is the fixed point set of some continuous self-mapping of Z. In this paper it is shown that there exists a one-dimensional contractible planar continuum having CIP whose wedge with itself at a specified point is contractible, planar, and does not have CIP.
DOI : 10.4153/CMB-1980-067-5
Mots-clés : 54F20, 54H25, 54B99, acyclic, complete invariance property, continuum, contractible, fixed point set, locally connected, one-dimensional, wedge. 
Martin, John R.; Jr, Sam B. Nadler. A Note on Fixed Point Sets and Wedges. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 453-455. doi: 10.4153/CMB-1980-067-5
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     title = {A {Note} on {Fixed} {Point} {Sets} and {Wedges}},
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     year = {1980},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-067-5/}
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