- Journal Details
- Format
- Journal
- eISSN
- 1898-9934
- ISSN
- 1426-2630
- First Published
- 09 Jun 2008
- Publication timeframe
- 4 times per year
- Languages
- English
Search
- Open Access
Basic Properties of Metrizable Topological Spaces
Page range: 201 - 205
Abstract
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 Lindelöf spaces and state the above theorem in this special case. We also introduce the concept of separation among two subsets (see [12]).
- Open Access
Small Inductive Dimension of Topological Spaces
Page range: 207 - 212
Abstract
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.
Abstract
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.
- Open Access
Small Inductive Dimension of Topological Spaces. Part II
Page range: 219 - 222
Abstract
In this paper we present basic properties of