Zariski topologyIn algebraic geometry and commutative algebra, the Zariski topology is a topology which is primarily defined by its closed sets. It is very different from topologies which are commonly used in real or complex analysis; in particular, it is not Hausdorff. This topology was introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological space.
Spectrum of a ringIn commutative algebra, the prime spectrum (or simply the spectrum) of a ring R is the set of all prime ideals of R, and is usually denoted by ; in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings . For any ideal I of R, define to be the set of prime ideals containing I. We can put a topology on by defining the to be This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈ R, define Df to be the set of prime ideals of R not containing f.
General topologyIn mathematics, 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 is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points.
Topological ringIn mathematics, a topological ring is a ring that is also a topological space such that both the addition and the multiplication are continuous as maps: where carries the product topology. That means is an additive topological group and a multiplicative topological semigroup. Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field.
Network topologyNetwork topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes.
Local ringIn mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises as the result of the localization of a ring at a prime ideal.
Ring networkA ring network is a network topology in which each node connects to exactly two other nodes, forming a single continuous pathway for signals through each node – a ring. Data travels from node to node, with each node along the way handling every packet. Rings can be unidirectional, with all traffic travelling either clockwise or anticlockwise around the ring, or bidirectional (as in SONET/SDH). Because a unidirectional ring topology provides only one pathway between any two nodes, unidirectional ring networks may be disrupted by the failure of a single link.
Human communicationHuman communication, or anthroposemiotics, is a field of study dedicated to understanding how humans communicate. Humans' ability to communicate with one another would not be possible without an understanding of what we are referencing or thinking about. Because humans are unable to fully understand one another's perspective, there needs to be a creation of commonality through a shared mindset or viewpoint. The field of communication is very diverse, as there are multiple layers of what communication is and how we use its different features as human beings.
Network throughputNetwork throughput (or just throughput, when in context) refers to the rate of message delivery over a communication channel, such as Ethernet or packet radio, in a communication network. The data that these messages contain may be delivered over physical or logical links, or through network nodes. Throughput is usually measured in bits per second (bit/s or bps), and sometimes in data packets per second (p/s or pps) or data packets per time slot. The system throughput or aggregate throughput is the sum of the data rates that are delivered to all terminals in a network.
Intercultural communicationIntercultural communication is a discipline that studies communication across different cultures and social groups, or how culture affects communication. It describes the wide range of communication processes and problems that naturally appear within an organization or social context made up of individuals from different religious, social, ethnic, and educational backgrounds. In this sense, it seeks to understand how people from different countries and cultures act, communicate, and perceive the world around them.
