/sci/ - Science & Math

>>11424380
Let [math]X\subset\mathbb{R}^{2}[/math] with polar coordinates [math]\{ (n,\theta) | n\in\omega , \theta\in \{ 0 \}\cup \{\frac{1}{n}\}_{n=1}^{\infty}\}[/math] and define a topology on [math]X[/math] by taking as basis all sets of the form [math]U\times V[/math] where [math]U[/math] is an open set in the right order topology on the non-negative integers and [math]V[/math] is open in [math]\{ 0 \}\cup \{\frac{1}{n}\}_{n=1}^{\infty}\subset \mathbb{R}[/math]. This is called the 'integer broom topology'.
>Properties
>"The integer broom space, together with the integer broom topology, is a compact topological space. It is a so-called Kolmogorov space, but it is neither a Fréchet space nor a Hausdorff space. The space is path connected, while neither locally connected nor arc connected."