closed topology
61Dunce hat (topology) — For the item of clothing designed to be humiliating, now rarely used, see dunce cap. To get a dunce hat, take a solid triangle and successively glue together all three sides with the indicated orientation. In topology, the dunce hat is a compact… …
62Either–or topology — In mathematics, the either–or topology is a topological structure defined on the closed interval [−1, 1] by declaring a set open iff it either does not contain {0} or does contain (−1, 1).References*Citation | last1=Steen | first1=Lynn Arthur |… …
63Brouwer's fixed point theorem — ▪ topology in mathematics, a theorem of algebraic topology (topology) that was stated and proved in 1912 by the Dutch mathematician L.E.J. Brouwer (Brouwer, Luitzen Egbertus Jan). Inspired by earlier work of the French mathematician Henri… …
64Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …
65Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …
66Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… …
67Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …
68Shape of the Universe — Edge of the Universe redirects here. For the Bee Gees song, see Edge of the Universe (song). The local geometry of the universe is determined by whether Omega is less than, equal to or greater than 1. From top to bottom: a spherical universe, a… …
69Interior algebra — In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and… …
70Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …
