# Category:Rational Number Space

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

Let $\Q$ be the set of rational numbers.

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

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

Then $\struct {\Q, \tau_d}$ is the **rational number space**.

## Subcategories

This category has only the following subcategory.

### R

## Pages in category "Rational Number Space"

The following 34 pages are in this category, out of 34 total.

### A

- Alexandroff Extension of Rational Number Space is Biconnected
- Alexandroff Extension of Rational Number Space is Connected
- Alexandroff Extension of Rational Number Space is not Hausdorff
- Alexandroff Extension of Rational Number Space is Sequentially Compact
- Alexandroff Extension of Rational Number Space is T1 Space

### C

### R

- Rational Number Space is Completely Normal
- Rational Number Space is Dense-in-itself
- Rational Number Space is Meager
- Rational Number Space is not Complete Metric Space
- Rational Number Space is not Locally Compact Hausdorff Space
- Rational Number Space is not Scattered
- Rational Number Space is not Weakly Sigma-Locally Compact
- Rational Number Space is Paracompact
- Rational Number Space is Second-Countable
- Rational Number Space is Separable
- Rational Number Space is Sigma-Compact
- Rational Number Space is Topological Space
- Rational Number Space is Topological Space/Proof 2
- Rational Number Space is Totally Separated
- Rational Number Space is Zero Dimensional
- Rational Numbers form Metric Space
- Rational Numbers form Metric Subspace of Real Numbers under Euclidean Metric
- Rationals are Dense in Compact Complement Topology
- Rationals are Everywhere Dense in Reals