We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting syste...

Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.

The concept of topological gyrogroups is a generalization group. In this work, ones prove that gyrogroup G metrizable iff has an {\omega}{\omega}-base and Frechet-Urysohn. Moreover, in gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn having are all weakly three-space properties with H closed L-subgyrogroup

Completely regular pseudo-compact spaces have been characterized in several ways. E. Hewitt [6, pp. 68-70] has given one characterization in terms of the Stone-Cech compactification and another in terms of the zero sets of continuous functions. J. Colmez [2; no proofs included] and I. Glicksberg [4] have obtained characterizations by means of a convergence property for sequences of continuous f...

Compact right topological groups arise in topological dynamics and in other settings. Following H. Furstenberg's seminal work on distal flows, R. Ellis and I. Namioka have shown that the compact right topological groups of dynamical type always admit a probability measure invariant under the continuous left translations; however, this invariance property is insufficient to identify a unique pro...

We propose solitons in a photonic topological insulator: self-localized wave packets forming topological edge states residing in the bulk of a nonlinear photonic topological insulator. These self-forming entities exhibit, despite being in the bulk, the property of unidirectional transport, similar to the transport their linear counterparts display on the edge of a topological insulator. In the ...