http://hdl.handle.net/11089/51618 Sun, 05 Apr 2026 20:46:31 GMT 2026-04-05T20:46:31Z https://dspace.uni.lodz.pl:443/bitstream/id/a17d4470-2b2d-45fa-a42d-a01482c61c1c/ http://hdl.handle.net/11089/51618 http://hdl.handle.net/11089/51687 Mathematical Methods in Region-Based Theories of Space: The Case of Whitehead Points Gruszczyński, Rafał Regions-based theories of space aim—among others—to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed, one should show that they are points of a geometrical or a topological space constructed in a specific way. This paper intends to show how the development of mathematical tools allows showing that Whitehead’s method of extensive abstraction provides a construction of objects that are fundamental building blocks of specific topological spaces. Mon, 04 Dec 2023 00:00:00 GMT http://hdl.handle.net/11089/51687 2023-12-04T00:00:00Z http://hdl.handle.net/11089/51689 \(L\)-Modules Saidi Goraghani, Simin; Borzooei, Rajab Ali In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-modules). Then we provide some examples and obtain some results on \(L\)-modules. Also, we present definitions of prime ideals of \(L\)-algebras and \(L\)-submodules (prime \(L\)-submodules) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules. Mon, 04 Dec 2023 00:00:00 GMT http://hdl.handle.net/11089/51689 2023-12-04T00:00:00Z http://hdl.handle.net/11089/51688 Stabilizers on \(L\)-algebras Rezaei, Gholam Reza; Aaly Kologani, Mona The main goal of this paper is to introduce the notion of stabilizers in \(L\)-algebras and develop stabilizer theory in \(L\)-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a \(CKL\)-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in \(CKL\)-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on \(L\)-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. Mon, 20 Nov 2023 00:00:00 GMT http://hdl.handle.net/11089/51688 2023-11-20T00:00:00Z http://hdl.handle.net/11089/51686 On Paracomplete Versions of Jaśkowski's Discussive Logic Mruczek-Nasieniewska, Krystyna; Petrukhin, Yaroslav; Shangin, Vasily Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p. Thu, 04 Jan 2024 00:00:00 GMT http://hdl.handle.net/11089/51686 2024-01-04T00:00:00Z