topologjik

Topologjik is the Albanian term for the mathematical field known in English as topology. It studies properties of spaces that are preserved under continuous deformations, such as stretching or bending, but not tearing or gluing. The subject provides a way to classify and compare shapes in a way that ignores exact measurements and focuses on qualitative structure.

Subfields of topologjik include point-set topology, which deals with open sets, convergence, and continuity; algebraic topology, which uses algebraic methods to define invariants such as homology and the fundamental group; differential topology, which studies smooth manifolds and maps; and geometric topology, which focuses on manifolds and their geometric properties.

Historical development began in the late 19th and early 20th centuries, with ideas contributed by mathematicians such as Georg Cantor, Henri Poincaré, and L. E. J. Brouwer. The field was further formalized by Paul Hausdorff and others, leading to a broad framework now central to many areas of mathematics.

Applications of topologjik appear across mathematics and science. In physics, topology informs concepts in quantum physics and general relativity. In computer science and data analysis, topological methods underpin persistent homology and shape recognition. The language of topology also appears in chemistry, economics, and network theory.

Related terms include topological invariants, continuity, compactness, and homeomorphism. In Albanian mathematics, topologjik is taught at university level and connects to both pure theory and applied research.