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In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.

Let

In topological dynamics, the Of course, the statement is preceded by the presentation of the concepts of an entropy structure and its superenvelopes, adapted from the case of

In this paper, we construct uniform structures on a E-compact semilattice of topological groups and study the structure of the uniform completion of a Hausdorff E-compact semilattice of topological groups.

The automorphisms of a two-generator free group \\mathsf F_2 acting on the space of orientation-preserving isometric actions of \\mathsf F_2 on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group \\Gamma on \\mathbb R ^3 by polynomial automorphisms preserving the cubic polynomial \\kappa _\\Phi (x,y,z) := -x^{2} -y^{2} + z^{2} + x y z -2 and an area form on the level surfaces \\kappa _{\\Phi}^{-1}(k).

It is common knowledge that any topological group that satisfies the lowest separation axiom, T0, is immediately Hausdorff and completely regular; however, this is not the case for normality. This motivates us to introduce the concept of pseudo-normal groups along with pseudo-Tychonoff topological groups as generalizations of the normality and Tychonoffness of topological groups, respectively. We show that every pseudo-normal (resp. pseudo-Tychonoff) topological group is normal (resp. Tychonoff). Generally, the reverse implication of the latter does not hold. Then, we discuss their main properties in detail. To clarify these properties, we provide some examples. Finally, we establish some other results.

This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. In this work we describe their

In this paper, the notion of a soft topological transformation group is defined and studied. For a soft topological transformation group, it is proven that a map from a soft topological space onto itself is soft homeomorphism. The collection of all soft homeomorphisms of the given soft topological space onto itself constitutes soft topological group under composition. Subsequently, it is proved that there is a homomorphism between soft topological group and the group structure on the collection of all soft homeomorphisms of given topological space. Subsequently, it is shown that the mapping space Map(Y,Y) is soft Hausdorff and verified that any subspace of the mapping space is soft Hausdorff. Additionally, it is proved that the set of all soft homeomorphisms on Y forms a soft discrete space, soft extremally disconnected space, soft Moscow space and a soft Moscow topological group. Later, it is shown that the map from a soft topological group to a mapping space is soft continuous. Finally, it is proved that distinct group structure generates distinct collection of all soft homeomorphisms of the specified soft topological space onto itself is a soft isomorphism.

We study conformal symmetry breaking differential operators which map differential forms on