On generalizations of topological games

Önal, Süleyman
We establish three games as generalizations of the Banach-Mazur game, the Choquet game and the point-open game. We find a characterization of compact scattered spaces by using one of the generalized games and show a relation between the other generalized games and domain representability.


On the strategies for NONEMPTY in topological games
Önal, Süleyman (Elsevier BV, 2020-06-01)
We prove that if NONEMPTY has a Markov strategy in the Choquet game on a space X, then the player has a 2-tactic in that game. We also prove that if NONEMPTY has a k-Markov strategy in the Choquet game on a space X which has a Noetherian base with countable rank, then the player has a k-tactic in that game. We show that if NONEMPTY has a winning strategy in the Choquet game on a space X which has one of the some special bases including sigma-locally countable bases, then the player has a 2-tactic in that ga...
On endomorphisms of surface mapping class groups
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.
Paracompactness of spaces which have covering properties weaker than paracompactness
Onal, S (Elsevier BV, 2001-07-16)
We prove that (i) a collectionwise normal, orthocompact, theta (m)-refinable, [m, N-0]-submetacompact space is paracompact, (ii) a collectionwise normal, [infinity, m]-paracompact [m, N-0]-submetacompact space is paracompact. This gives a sufficient condition for the paracompactness of para-Lindelof, collectionwise normal spaces.
On homotopy groups of real algebraic varieties and their complexifications
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.
Tight contact structures on hyperbolic three-manifolds
Arıkan, Mehmet Fırat (Elsevier BV, 2017-11-01)
Let Sigma(g) denote a closed orientable surface of genus g >= 2. We consider a certain infinite family of Sigma(g)-bundles over circle whose monodromies are taken from some collection of pseudo-Anosov diffeomorphisms. We show the existence of tight contact structure on every closed 3-manifold obtained via rational r-surgery along a section of any member of the family whenever r not equal 2g - 1. Combining with Thurston's hyperbolic Dehn surgery theorem, we obtain infinitely many hyperbolic closed 3-manifold...
Citation Formats
S. Önal and Ç. VURAL, “On generalizations of topological games,” TOPOLOGY AND ITS APPLICATIONS, pp. 524–533, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46751.