Coffee mug in the context of Drink

Merchandising is any practice which contributes to the sale of products ("merch" colloquially) to a retail consumer. At a retail in-store level, merchandising refers to displaying products that are for sale in a creative way that entices customers to purchase more items or products.

In retail commerce, visual display merchandising means merchandise sales using product design, selection, packaging, pricing, and display that stimulates consumers to spend more. This includes disciplines and discounting, physical presentation of products and displays, and the decisions about which products should be presented to which customers at what time. Often in a retail setting, creatively tying in related products or accessories is a great way to entice consumers to purchase more.

In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.

Very roughly speaking, a topological space is a geometric object, and a homeomorphism results from a continuous deformation of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not. However, this description can be misleading. Some continuous deformations do not produce homeomorphisms, such as the deformation of a line into a point. Some homeomorphisms do not result from continuous deformations, such as the homeomorphism between a trefoil knot and a circle. Homotopy and isotopy are precise definitions for the informal concept of continuous deformation.