Partial actions on convergence spaces
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Nathaniel Adu
,
Piotr Mikusiński
Abstract
Continuous partial actions and continuous enveloping actions are investigated in the category of convergence spaces. Product and quotient constructions are considered. Further, it is shown that a continuous partial action on a convergence space can be extended to a continuous partial action on a compactification of the convergence space.
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Dedicated to Professor D.C. Kent and to the memory of Professor Roman Frič
( Communicated by L'ubica Holá)
References
[1] ABADIE, F.: Enveloping actions and Takai duality for partial actions, J. Funct. Anal. 197 (2003), 14–67.10.1016/S0022-1236(02)00032-0Suche in Google Scholar
[2] BOUSTIQUE, H.— MIKUSIŃSKI, P.—RICHARDSON, G.: Convergence semigroup actions: generalized quotients, Appl. Gen. Topol. 10 (2009), 173–186.10.4995/agt.2009.1731Suche in Google Scholar
[3] BOUSTIQUE, H.—MIKUSIŃSKI, P.—RICHARDSON, G.: Convergence semigroup categories, Appl. Gen. Topol. 11 (2010), 67–88.Suche in Google Scholar
[4] COLEBUNDERS, E.—BOUSTIQUE, H.—MIKUSIŃSKI, P.—RICHARDSON, G.: Convergence approach spaces: actions, Appl. Categ. Structures 24 (2016), 147–161.10.1007/s10485-015-9390-2Suche in Google Scholar
[5] DE VRIES, J.: Topological Transformation Groups 1: A Categorical Approach. Mathematical Centre Tracts 65, Mathematisch Centrum, Amsterdam, 1975.Suche in Google Scholar
[6] FRIČ, R.—MCKENNON, K.—RICHARDSON, G.: Sequential Convergence in C(X). Convergence Structures and Applications to Analysis, Akademie-Verlag, Berlin, 1980, 57–65.Suche in Google Scholar
[7] KATSEVICH, A.—MIKUSIŃSKI, P.: On De Graaf spaces of pseudoquotients, Rocky Mountain J. Math. 45 (2015), 1445–1455.10.1216/RMJ-2015-45-5-1445Suche in Google Scholar
[8] KENT, D. C.—RICHARDSON, G.: Locally compact convergence spaces, Michigan Math. J. 22 (1975), 353–360.10.1307/mmj/1029001576Suche in Google Scholar
[9] KENT, D. C.—RICHARDSON, G.: Some product theorems for convergence spaces, Math. Nachr. 87 (1979), 43–51.10.1002/mana.19790870106Suche in Google Scholar
[10] MEGRELISHVILI, M.—SCARR, T.: Constructing Tychonoff G-spaces which are not G-Tychonoff, Special issue on topological groups, Topology Appl. 86 (1998), 69–81.10.1016/S0166-8641(97)00125-9Suche in Google Scholar
[11] MIKUSIŃSKI, P.: Generalized quotients with applications in analysis, Methods Appl. Anal. 10 (2003), 377–386.10.4310/MAA.2003.v10.n3.a4Suche in Google Scholar
© 2022 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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- Existence of positive solutions for boundary value problems with p-Laplacian operator
Artikel in diesem Heft
- Regular Papers
- Variants of Booleanness: Congruences of a partial frame versus those of its free frame
- Models, coproducts and exchangeability: Notes on states on Baire functions
- Inverse tangent series involving pell and pell-lucas polynomials
- A new family of two-variable polynomials based on hermite polynomials
- Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
- On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
- Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
- Stability criteria for systems of two first-order linear ordinary differential equations
- A perturbed eigenvalue problem in exterior domain
- On extensions of bilinear maps
- Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
- Weighted composition operators from the Besov space into nth weighted type spaces
- Fuzzy ideal topological vector spaces
- Partial actions on convergence spaces
- On quasi-small loop groups
- Topologies generated by symmetric porosity on normed spaces
- The Alpha Power Rayleigh-G family of distributions
- An alternative for Laplace Birnbaum-Saunders distribution
- Existence of positive solutions for boundary value problems with p-Laplacian operator
