As of my last update in October 2023, Serbia is divided into several statistical regions for the purposes of economic analysis, planning, and development. These statistical regions are recognized by the statistical office of Serbia and facilitate the collection and interpretation of data related to various socio-economic activities. Serbia is organized into the following statistical regions: 1. **Belgrade Region** - This includes the capital city, Belgrade, which is the political, cultural, and economic center of Serbia.

In topology, theorems are statements that have been proven to be true based on axioms and previously established theorems within the framework of topology. Topology is a branch of mathematics that studies properties of space that are preserved under continuous transformations.

General topology, also known simply as topology, is a branch of mathematics that deals with the properties of space that are preserved under continuous transformations. It provides the foundational language and concepts for many areas of mathematics by introducing notions such as continuity, compactness, connectedness, and convergence without relying on the traditional metrics of distance from geometry. Key concepts in general topology include: 1. **Topological Spaces**: A set equipped with a collection of open subsets that satisfy certain axioms.

In group theory, the **center** of a group \( G \), often denoted as \( Z(G) \), is defined as the set of elements in \( G \) that commute with every other element in the group.

Topological spaces are fundamental objects of study in topology, a branch of mathematics focused on the properties of space that are preserved under continuous transformations. Here are some key properties and concepts associated with topological spaces: 1. **Open and Closed Sets**: - A topology on a set \(X\) is a collection of subsets of \(X\) (called open sets) that includes the empty set and \(X\) itself, and is closed under arbitrary unions and finite intersections.

In mathematics, particularly in the field of group theory and algebra, a class automorphism refers to a specific type of automorphism of a group, particularly in the context of a class of structures, such as groups or rings. ### Definition of Automorphism An **automorphism** is an isomorphism from a mathematical structure to itself. In simpler terms, it's a bijective (one-to-one and onto) mapping of a structure that preserves the operations defined on that structure.

Zu Chongzhi was a Chinese mathematician and astronomer who lived during the Northern and Southern dynasties period (circa 429–500 AD). He is best known for his work in mathematics, particularly for his calculation of the value of π (pi). Zu Chongzhi calculated π to be approximately 3.1415926, which was remarkably accurate for his time and remained the most precise approximation for over a thousand years.

The Fellows of the Association for Women in Mathematics (AWM) is an honorary designation that recognizes women who have made significant contributions to the field of mathematics. This initiative is aimed at highlighting the achievements of women mathematicians, promoting their work, and encouraging the inclusion of women in mathematics. The fellowship honors those who have demonstrated excellence in research, teaching, or service to the community, and recipients are typically nominated by their peers.

The 18th century was a pivotal time for the development of physics, and several British scientists made significant contributions during this period. Here are some notable British physicists from the 18th century: 1. **Isaac Newton (1643-1727)** - Although he was primarily active in the late 17th century, Newton's influence continued throughout the 18th century. His work in physics, especially his laws of motion and universal gravitation, laid the groundwork for classical mechanics.

Cohomological dimension is a concept from algebraic topology, algebraic geometry, and homological algebra that relates to the size of a space or algebraic object as measured by its cohomology groups. It serves as a measure of the "complexity" of a topological space or algebraic structure in terms of the ability to compute its cohomology.

In the 18th century, Hungary was part of the Austro-Hungarian Empire, and while it may not have been a primary center for physics compared to places like France or England, there were still notable contributions from Hungarian scientists during this period. One of the most significant figures of that time was: ### 1.