By William F. Basener

**Discover a distinct and sleek therapy of topology using a cross-disciplinary approach**
Implemented lately to appreciate assorted subject matters, equivalent to mobile biology, superconductors, and robotic movement, topology has been reworked from a theoretical box that highlights mathematical conception to a subject matter that performs a becoming position in approximately all fields of clinical research. relocating from the concrete to the summary, Topology and Its functions screens either the sweetness and software of topology, first proposing the necessities of topology via its rising function in the new frontiers in research.

Filling a niche among the instructing of topology and its sleek makes use of in real-world phenomena, Topology and Its purposes is geared up round the mathematical concept of topology, a framework of rigorous theorems, and transparent, stylish proofs.

This booklet is the 1st of its variety to give functions in special effects, economics, dynamical platforms, condensed subject physics, biology, robotics, chemistry, cosmology, fabric technological know-how, computational topology, and inhabitants modeling, in addition to different parts of technological know-how and engineering. a lot of those functions are offered in not obligatory sections, permitting an teacher to customise the presentation.

The writer offers a range of topological parts, together with point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. themes inside those parts include:

- Open sets
- Compactness
- Homotopy
- Surface classification
- Index conception on surfaces
- Manifolds and complexes
- Topological groups
- The primary staff and homology

Special "core instinct" segments through the booklet in short clarify the fundamental instinct necessary to knowing numerous themes. A beneficiant variety of figures and examples, lots of which come from functions corresponding to liquid crystals, house probe info, and special effects, are all to be had from the publisher's internet site.