mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of...

In topology, a topological space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces...

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...

topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact...

Hausdorff space is normal. See also quasicompact. Compact-open topology The compact-open topology on the set C(X, Y) of all continuous maps between two...

The (natural) compact open topology on the resulting set of continuous functions is sometimes referred to as the semicontinuous topology. Additionally...

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks...

harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For...

generalizes the idea of uniform convergence. It is associated with the compact-open topology. Let ( X , T ) {\displaystyle (X,{\mathcal {T}})} be a topological...

family of functions from a compactly generated Hausdorff space into a uniform space to be compact in the compact-open topology; see Kelley (1991, page 234)...

closed (respectively, weakly compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise, functions are sometimes...

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

Uniform norm Weak topology Strong topology Hilbert cube Lower limit topology Sorgenfrey plane Real tree Compact-open topology Zariski topology Kuratowski closure...

In mathematics, the lower limit topology or right half-open interval topology is a topology defined on R {\displaystyle \mathbb {R} } , the set of real...

topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is...

arc, and the free differential calculus. He also identified the compact-open topology on function spaces as being particularly appropriate for homotopy...

component spaces are compact, the box topology on their Cartesian product will not necessarily be compact, although the product topology on their Cartesian...

general topology, a field of mathematics. Alexandrov topology Cantor space Co-kappa topology Cocountable topology Cofinite topology Compact-open topology Compactification...

\operatorname {Homeo} (X).} This group can be given a topology, such as the compact-open topology, which under certain assumptions makes it a topological...

f:X\to Y} has a natural topology called the compact-open topology. A normal family is a pre-compact subset with respect to this topology. If Y is a metric space...

spaces. A commonly used example is the compact-open topology, e.g. loop space. Also available is the product topology on the space of set theoretic functions...

connectedness, compactness, and various separation axioms. For algebraic invariants see algebraic topology. Complete Heyting algebra – The system of all open sets...

subsets are open. Indiscrete topology, chaotic topology, or Trivial topology − Only the empty set and its complement are open. Cocountable topology Given a...

endowed with the topology given by uniform convergence on compact sets (that is, the topology induced by the compact-open topology on the space of all...

{\textstyle \left(X,B\right)\rightarrow \left(Y,A\right)} (with the compact-open topology on the mapping space) is an ANR. It follows, for example, that the...

In general topology, an Alexandrov topology is a topology in which the intersection of an arbitrary family of open sets is open (while the definition of...

field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff...

In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional...

{Prim} (A).} The hull-kernel topology is easy to describe abstractly, but in practice for C*-algebras associated to locally compact topological groups, other...

homeomorphism group can be given a topology, such as the compact-open topology. In the case of regular, locally compact spaces the group multiplication is...