There is no domain representable dense proper subsemigroup of a topological group

We prove that the only domain representable dense subsemigroup of a topological group is itself. Consequently, we obtain that every domain representable subgroup of a topological group is closed.


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Korkmaz, Mustafa (Elsevier BV, 2001-05-01)
In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
An obstruction to the existence of real projective structures
Coban, Hatice (Elsevier BV, 2019-09-15)
In this short note, we give an obstruction to obtain examples of higher dimensional manifolds with infinite fundamental groups, including the infinite cyclic group Z, admitting no real projective structure.
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
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Ozan, Yıldıray (Springer Science and Business Media LLC, 2004-10-01)
Let X-0 be a topological component of a nonsingular real algebraic variety and i : X --> X-C is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i: X-0 --> X-C and obtain several results using rational homotopy theory and other standard tools of homotopy theory.
Some cardinal invariants on the space C-alpha (X, Y)
Onal, S; Vural, C (Elsevier BV, 2005-05-14)
Let C-alpha (X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where a is a hereditarily closed, compact network on X such that closed under finite unions. We define two properties (E1) and (E2) on the triple (alpha, X, Y) which yield new equalities and inequalities between some cardinal invariants on C-alpha (X, Y) and some cardinal invariants on the spaces X, Y such as:
Citation Formats
S. Önal, “There is no domain representable dense proper subsemigroup of a topological group,” TOPOLOGY AND ITS APPLICATIONS, pp. 79–84, 2017, Accessed: 00, 2020. [Online]. Available: