There are actually more than a definition of the open set in topology. They are:
In point-set topology, the properties of the set S are:X and ∅ belongs to the set S.The intersection of any subsets belongs to the set S.The union of any subsets belongs to the set S.For instance:Let τ = {X,∅}. Then, it's the topology. We call that the trivial or discrete topology. If the set is indiscrete topology, then it contains infinitely many elements!
Advantages include: Its easy to set up, handle, and implement, It is best-suited for small networks and its less costly. There 3 types of topology which are; ring, bus and star topology.
John D. Baum has written: 'Elements of point set topology' -- subject(s): Topology
Steven A. Gaal has written: 'Point set topology'
Ring topology is the passive topology in computer networks
A star topology is best for a classroom environment. This topology is easy to set up and manage, and it allows for easy expansion of the network. Additionally, it is less susceptible to network outages due to a single point of failure.
A switch topology is an organizational representation of the channels and relays in a switch module. The topology establishes the default states for all relays in a module and defines the channel names. Some switches can use multiple topologies or variations of each topology type. Some terminal blocks or accessories may force the switch to use a given topology or set of topologies. GHOUL
There are three axioms that must be satisfied for a collection of subsets, t, of set B to be called a topology on B.1) Both B and the empty set, Ø, must be members of t.2) The intersection of any two members of t must also be a member of t.3) The union of any family of members of t must also be a member of t.If these axioms are met, the members of t are known as t-open or simply open, subsets of B.See related links.
Topology
1.bus topology, 2.ring topology, 3.mesh topology, 4.star topology, 5.hybrid topology
star topology,bus topology,ring topology,mesh topology etc...
Ring Topology, Mesh Topology, Bus Topology, Star Topology