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Token Ring (802.5) networks imitate a ring at layer 2 but use a physical star at layer 1. "Rings prevent collisions." The term "ring" only refers to the layout of the cables. It is true that there are no collisions on an IBM Token Ring, but this is because of the layer 2 Media Access Control method, not the physical topology (which again is a ...
A network's logical topology is not necessarily the same as its physical topology. For example, the original twisted pair Ethernet using repeater hubs was a logical bus topology carried on a physical star topology. Token Ring is a logical ring topology, but is wired as a physical star from the media access unit.
During normal operation, the network works in the Ring-Closed status (Figure 1). In this status, one of the MRM ring ports is blocked, while the other is forwarding. Conversely, both ring ports of all MRCs are forwarding. Loops are avoided because the physical ring topology is reduced to a logical line topology.
A ringed space (,) is a topological space together with a sheaf of rings on .The sheaf is called the structure sheaf of .. A locally ringed space is a ringed space (,) such that all stalks of are local rings (i.e. they have unique maximal ideals).
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
X is homeomorphic to the spectrum of a commutative ring. X is the topological space determined by a Priestley space . X is a T 0 space whose frame of open sets is coherent (and every coherent frame comes from a unique spectral space in this way).
A more complicated example is the -adic topology on a ring and its modules. Let I {\displaystyle I} be an ideal of a ring R . {\displaystyle R.} The sets of the form x + I n {\displaystyle x+I^{n}} for all x ∈ R {\displaystyle x\in R} and all positive integers n , {\displaystyle n,} form a base for a topology on R {\displaystyle R} that makes ...
Highly structured ring spectra have better formal properties than multiplicative cohomology theories – a point utilized, for example, in the construction of topological modular forms, and which has allowed also new constructions of more classical objects such as Morava K-theory.