$\operatorname{PL}(M)$ admits no Polish group topology

2017 ◽  
Vol 238 (3) ◽  
pp. 285-295
Author(s):  
Kathryn Mann
Keyword(s):  
Group Topology ◽  
Polish Group

scholarly journals Full groups of minimal homeomorphisms and Baire category methods

2014 ◽  
Vol 36 (2) ◽  
pp. 550-573
Author(s):  
TOMÁS IBARLUCÍA ◽  
JULIEN MELLERAY
Keyword(s):  
Baire Category ◽  
Full Group ◽  
Group Topology ◽  
Cantor Space ◽  
Polish Group ◽  
Minimal Homeomorphisms

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space$X$, showing that these groups do not admit a compatible Polish group topology and, in the case of$\mathbb{Z}$-actions, are coanalytic non-Borel inside$\text{Homeo}(X)$. We point out that the full group of a minimal homeomorphism is topologically simple. We also study some properties of the closure of the full group of a minimal homeomorphism inside$\text{Homeo}(X)$.

scholarly journals Uniqueness of Polish group topology

2008 ◽  
Vol 155 (9) ◽  
pp. 992-999 ◽  
Author(s):  
Paul Gartside ◽  
Bojana Pejić
Keyword(s):  
Group Topology ◽  
Polish Group

scholarly journals A nonlinear maximal group topology

2012 ◽  
Vol 229 (4) ◽  
pp. 2415-2426
Author(s):  
Yevhen Zelenyuk
Keyword(s):  
Group Topology ◽  
Maximal Group

scholarly journals A note on the duality of locally compact groups

1968 ◽  
Vol 9 (2) ◽  
pp. 87-91 ◽  
Author(s):  
J. W. Baker
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Group Topology ◽  
Locally Compact ◽  
Natural Way

Let H be a group of characters on an (algebraic) abelian group G. In a natural way, we may regard G as a group of characters on H. In this way, we obtain a duality between the two groups G and H. One may pose several problems about this duality. Firstly, one may ask whether there exists a group topology on G for which H is precisely the set of continuous characters. This question has been answered in the affirmative in [1]. We shall say that such a topology is compatible with the duality between G and H. Next, one may ask whether there exists a locally compact group topology on G which is compatible with a given duality and, if so, whether there is more than one such topology. It is this second question (previously considered by other authors, to whom we shall refer below) which we shall consider here.

scholarly journals Group, basic assumptions and complexity science

2018 ◽  
Vol 52 (1) ◽  
pp. 3-22 ◽  
Author(s):  
Giulio de Felice ◽  
Giuseppe De Vita ◽  
Alessandro Bruni ◽  
Assunta Galimberti ◽  
Giulia Paoloni ◽  
...  
Keyword(s):  
Critical Points ◽  
Work Group ◽  
Complexity Science ◽  
Group Topology ◽  
Basic Assumptions ◽  
Psychoanalytic Literature ◽  
Group Mentality

This article represents the first complete systematization of the basic assumptions as theorized by Wilfred R. Bion and post-Bionian authors. The authors reviewed, compared and systematized all the Bionian developments concerning the basic assumptions taking the prevailing anxieties, group topology, leader peculiarities, interactions with the work-group mentality into account. The analysis evinced five main ba(s) and five subsets (i.e. their features resemble one of the five main basic assumptions). Briefly, in the first paragraph the authors summarize Bionian thought and its underlying logical criteria while in the second they reviewed all the new proposals for basic assumptions emerging from the psychoanalytic literature (i.e. Lawrence, Bain and Gould, 1996; Romano, 1997; Sandler, 2002; Sarno, 1999; Turquet, 1974; Hopper, 2009). In conclusion the authors focus on the main strengths and critical points of the systematization. In the last section ‘Promising developments’ they address the methodology of the study of basic assumptions, its main features and potential developments. The article rounds off with a clinical appendix.

The Meet Operator in the Lattice of Group Topologies

1986 ◽  
Vol 29 (4) ◽  
pp. 478-481
Author(s):  
Bradd Clark ◽  
Victor Schneider
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Locally Compact Group ◽  
Group Topology ◽  
Locally Compact ◽  
Hausdorff Topology ◽  
Lattice Of Topologies ◽  
Group Form ◽  
Complemented Lattice ◽  
Infinite Abelian Group

AbstractIt is well known that the lattice of topologies on a set forms a complete complemented lattice. The set of topologies which make G into a topological group form a complete lattice L(G) which is not a sublattice of the lattice of all topologies on G.Let G be an infinite abelian group. No nontrivial Hausdorff topology in L(G) has a complement in L(G). If τ1 and τ2 are locally compact topologies then τ1Λτ2 is also a locally compact group topology. The situation when G is nonabelian is also considered.

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