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Fixed point sets of homeomorphisms of metric products
In this paper it is investigated as to when a nonempty closed subset A of a metric product X containing intervals or spheres as factors can be the fixed point set of an autohomeomorphism of X. It isExpand
COMPACT GROUPS AND FIXED POINT SETS
Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It isExpand
(L)-Semigroup Sums
TLDR
It is shown that no (L)-semigroup sum of dimension less than or equal to five admits an H-space structure, nor does any (L)+T sum obtained from (L-semigroups having an Abelian boundary cannot be a retract of a topological group. Expand
Möbius manifolds, monoids, and retracts of topological groups
The definition for an $$n$$n-dimensional Möbius manifold is given; $$n=2$$n=2 yields the classical Möbius band. For $$n=1, 2$$n=1,2 or $$4$$4, these manifolds are compact topological monoids, forExpand
Covering space semigroups and retracts of compact Lie groups
If B is a compact connected Lie group and N a finite central subgroup, let $${f\colon B\to B/N}$$f:B→B/N be the associated covering morphism. The mapping cylinder $${{\mathrm{MC}}(f)}$$MC(f) is aExpand
Fixed point sets of $1$-dimensional Peano continua.
It is shown that every nonempty closed subset of a 1dimensional Peano continuum X is the fixed point set of some continuous self-mapping of X.
A generalization of absolute retracts
In this paper the concept of an absolute retract is generalized to a new concept which we call an absolute approximate retract. It is shown that for the class of compact metric spaces, the class ofExpand
Topology Proceedings 39 (2012) pp. 185-194: Topological Left-loops
In this note we define the concept of a topological leftloop which generalizes the notion of a topological loop, and we show that it is a useful tool in unifying arguments on traditional spaces of aExpand
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