Frai 33+ Indiscrete Topology Example

Frai 33+ Indiscrete Topology Example. Recall from the topological spaces page that a set $x$ and a collection $\tau$ of subsets of $x we will now look at two rather trivial topologies known as the discrete topologies and the indiscrete. The indiscrete topology on x is the weakest topology, so it has the most compact sets. Is called the indiscrete topological space or simply an indiscrete space. If every infinite subset of $x$ is declared open, then this topology is the discrete topology, not the indiscrete one.

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The only closed subsets are the whole space and the empty subset. Network topology is the layout of a network. Is called the indiscrete topological space or simply an indiscrete space. For a trivial example, let x be an infinite set with the indiscrete topology; To see this, take an arbitrary countably infinite subset $y$ of $x$. The stacks project, example 7.6.6. A topological space is termed an indiscrete space if it satisfies the following equivalent conditions: However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using grothendieck topologies.