In general topology and related areas of mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set X , {\displaystyle...

to: the final topology on the disjoint union the topology arising from a norm the strong operator topology the strong topology (polar topology), which...

In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can...

In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

topology, f is continuous with respect to this topology if and only if the existing topology is coarser than the final topology on S. Thus, the final...

general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which...

In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct)...

X {\displaystyle X} to be compactly generated if its topology coincides with the final topology with respect to this family of maps. And other variations...

Topology of a transmembrane protein refers to locations of N- and C-termini of membrane-spanning polypeptide chain with respect to the inner or outer sides...

obtained by placing the initial topology on (L, φ : L → F). Dually, colimits in Top are obtained by placing the final topology on the corresponding colimits...

The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics....

In any domain of mathematics, a space has a natural topology if there is a topology on the space which is "best adapted" to its study within the domain...

Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions...

relation of a topological structure to other one(s) Final topology Discrete topology, the most fine topology possible on a given set This disambiguation page...

In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent...

certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular...

{\displaystyle C_{c}^{\infty }(U),} is endowed with a certain topology, called the canonical LF-topology, that makes C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)}...

toxins. All beta-barrel transmembrane proteins have simplest up-and-down topology, which may reflect their common evolutionary origin and similar folding...

In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets...

In topology, especially algebraic topology, the cone of a topological space X {\displaystyle X} is intuitively obtained by stretching X into a cylinder...

In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the...

Applied topology explains how large molecules reach their final shapes and how biological molecules achieve their activity. Circuit topology is a topological...

If it exists, then the final topology on X in C {\displaystyle {\mathcal {C}}} , also called the colimit or inductive topology in C {\displaystyle {\mathcal...

primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains...

The circuit topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values...

{\displaystyle \mathbb {K} ^{\infty }} a final topology τ ∞ {\displaystyle \tau ^{\infty }} , defined to be the finest topology on K ∞ {\displaystyle \mathbb {K}...

limits in the category of topological spaces are given by placing the final topology on the underlying set-theoretic direct limit. An ind-scheme is an inductive...