http://hdl.handle.net/11320/3538 2026-06-01T15:23:57Z 2026-06-01T15:23:57Z Pąk, Karol http://hdl.handle.net/11320/3544 2017-10-05T22:45:12Z 2009-01-01T00:00:00Z

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 Pąk, Karol http://hdl.handle.net/11320/3545 2017-10-05T22:45:17Z 2009-01-01T00:00:00Z

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 Pąk, Karol http://hdl.handle.net/11320/3547 2017-10-05T22:45:17Z 2009-01-01T00:00:00Z

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 Liang, Xiquan Li, Dailu http://hdl.handle.net/11320/3546 2017-10-05T22:45:17Z 2009-01-01T00:00:00Z

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