# Category:Irrational Number Space

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This category contains results about the irrational number space in the context of Topology.

Let $\mathbb I := \R \setminus \Q$ be the set of irrational numbers.

Let $d: \mathbb I \times \mathbb I \to \R$ be the Euclidean metric on $\mathbb I$.

Let $\tau_d$ be the topology on $\mathbb I$ induced by $d$.

Then $\struct {\mathbb I, \tau_d}$ is the **irrational number space**.

## Pages in category "Irrational Number Space"

The following 20 pages are in this category, out of 20 total.

### C

### I

- Irrational Number Space is Complete Metric Space
- Irrational Number Space is Completely Normal
- Irrational Number Space is Dense-in-itself
- Irrational Number Space is Non-Meager
- Irrational Number Space is not Locally Compact Hausdorff Space
- Irrational Number Space is not Scattered
- Irrational Number Space is not Weakly Sigma-Locally Compact
- Irrational Number Space is Paracompact
- Irrational Number Space is Second-Countable
- Irrational Number Space is Separable
- Irrational Number Space is Topological Space
- Irrational Number Space is Totally Separated
- Irrational Number Space is Zero Dimensional
- Irrational Numbers form Metric Space
- Irrationals are Everywhere Dense in Reals