On ordered topological vector groups - new results
Апстракт
The theory of ordered topological vector spaces has been treated in a great number of articles and books. On the other hand, topological vector groups were introduced and studied by D. A. Raikov [On B-complete topological vector groups, Studia Math. 31 (1968), 296-305] and P. S. Kenderov [On topological vector groups, Mat. Sb. 10 (1970), 531-546]. These are vector spaces with a topology in which addition is continuous, but multiplication by scalars is continuous only if the scalar field is taken with the discrete topology. In this paper we introduce ordered topological vector groups and investigate their structure, in particular exploring them in the case when they need not be locally convex.
Кључне речи:
Topological vector space / locally convex space / ordered vector space / Riesz space / open decomposition propertyИзвор:
Journal of nonlinear and convex analysis, 2022, 23, 6, 1231-1254Колекције
Институција/група
VinčaTY - JOUR AU - Kalderburg, Zoran AU - Fabiano, Nicola AU - Mirkov, Nikola S. AU - Radenović, Stojan PY - 2022 UR - https://vinar.vin.bg.ac.rs/handle/123456789/11718 AB - The theory of ordered topological vector spaces has been treated in a great number of articles and books. On the other hand, topological vector groups were introduced and studied by D. A. Raikov [On B-complete topological vector groups, Studia Math. 31 (1968), 296-305] and P. S. Kenderov [On topological vector groups, Mat. Sb. 10 (1970), 531-546]. These are vector spaces with a topology in which addition is continuous, but multiplication by scalars is continuous only if the scalar field is taken with the discrete topology. In this paper we introduce ordered topological vector groups and investigate their structure, in particular exploring them in the case when they need not be locally convex. T2 - Journal of nonlinear and convex analysis T1 - On ordered topological vector groups - new results VL - 23 IS - 6 SP - 1231 EP - 1254 UR - https://hdl.handle.net/21.15107/rcub_vinar_11718 ER -
@article{ author = "Kalderburg, Zoran and Fabiano, Nicola and Mirkov, Nikola S. and Radenović, Stojan", year = "2022", abstract = "The theory of ordered topological vector spaces has been treated in a great number of articles and books. On the other hand, topological vector groups were introduced and studied by D. A. Raikov [On B-complete topological vector groups, Studia Math. 31 (1968), 296-305] and P. S. Kenderov [On topological vector groups, Mat. Sb. 10 (1970), 531-546]. These are vector spaces with a topology in which addition is continuous, but multiplication by scalars is continuous only if the scalar field is taken with the discrete topology. In this paper we introduce ordered topological vector groups and investigate their structure, in particular exploring them in the case when they need not be locally convex.", journal = "Journal of nonlinear and convex analysis", title = "On ordered topological vector groups - new results", volume = "23", number = "6", pages = "1231-1254", url = "https://hdl.handle.net/21.15107/rcub_vinar_11718" }
Kalderburg, Z., Fabiano, N., Mirkov, N. S.,& Radenović, S.. (2022). On ordered topological vector groups - new results. in Journal of nonlinear and convex analysis, 23(6), 1231-1254. https://hdl.handle.net/21.15107/rcub_vinar_11718
Kalderburg Z, Fabiano N, Mirkov NS, Radenović S. On ordered topological vector groups - new results. in Journal of nonlinear and convex analysis. 2022;23(6):1231-1254. https://hdl.handle.net/21.15107/rcub_vinar_11718 .
Kalderburg, Zoran, Fabiano, Nicola, Mirkov, Nikola S., Radenović, Stojan, "On ordered topological vector groups - new results" in Journal of nonlinear and convex analysis, 23, no. 6 (2022):1231-1254, https://hdl.handle.net/21.15107/rcub_vinar_11718 .