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Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open...

empty set, and the whole set itself. A set in which such a collection is given is called a topological space, and the collection is called a topology. These...

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

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...

mathematics, pointless topology, also called point-free topology (or pointfree topology) and locale theory, is an approach to topology that avoids mentioning...

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...

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

In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology, called the product topology. This space...

real numbers form an initial unbounded totally ordered set that is connected in the order topology (defined below). Ordered fields are totally ordered by...

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe...

the mathematical field of topology; see Full set A property of functors in the mathematical field of category theory; see Full and faithful functors Satiety...

of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space. A category...

left adjoint D : Set → Top which equips a given set with the discrete topology, and a right adjoint I : Set → Top which equips a given set with the indiscrete...

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 in...

In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that...

defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as...

differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct...

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean...

from considering the topology generated by the complexes of a field of sets. (It is just one of notable topologies on the given set of points; it often...

mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, is a topology on B(H), the space of bounded...