http://hdl.handle.net/11320/3538 2026-06-01T14:17:28Z http://hdl.handle.net/11320/3544 Tytuł: Basic Properties of Metrizable Topological Spaces Autorzy: Pąk, Karol Abstrakt: We continue Mizar formalization of general topology according to the book [11] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also define Lindel¨of spaces and state the above theorem in this special case. We also introduce the concept of separation among two subsets (see [12]). 2009-01-01T00:00:00Z http://hdl.handle.net/11320/3545 Tytuł: Small Inductive Dimension of Topological Spaces Autorzy: Pąk, Karol Abstrakt: We present the concept and basic properties of the Menger-Urysohn small inductive dimension of topological spaces according to the books [7]. Namely, the paper includes the formalization of main theorems from Sections 1.1 and 1.2. 2009-01-01T00:00:00Z http://hdl.handle.net/11320/3547 Tytuł: Small Inductive Dimension of Topological Spaces. Part II Autorzy: Pąk, Karol Abstrakt: In this paper we present basic properties of n-dimensional topological spaces according to the book [10]. In the article the formalization of Section 1.5 is completed. 2009-01-01T00:00:00Z http://hdl.handle.net/11320/3546 Tytuł: On Rough Subgroup of a Group Autorzy: Liang, Xiquan; Li, Dailu Abstrakt: This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group. 2009-01-01T00:00:00Z