# Category:Either-Or Topology

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This category contains results about Either-Or Topology.

Let $S = \left[{-1 \,.\,.\, 1}\right]$ be the closed interval on the real number line from $-1$ to $1$.

Let $\tau \subseteq \mathcal P \left({S}\right)$ be a subset of the power set of $S$ such that, for any $H \subseteq S$:

- $H \in \tau \iff \left({\left\{{0}\right\} \nsubseteq H \lor \left({-1 \,.\,.\, 1}\right) \subseteq H}\right)$

where $\lor$ is the inclusive-or logical connective.

Then $\tau$ is the **either-or topology**, and $T = \left({S, \tau}\right)$ is the **either-or space**

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Either-Or Topology"

The following 18 pages are in this category, out of 18 total.

### E

- Either-Or Topology is First-Countable
- Either-Or Topology is Lindelöf
- Either-Or Topology is Locally Connected
- Either-Or Topology is Locally Path-Connected
- Either-Or Topology is Non-Meager
- Either-Or Topology is not Locally Arc-Connected
- Either-Or Topology is not Separable
- Either-Or Topology is not T1
- Either-Or Topology is not T3
- Either-Or Topology is Scattered
- Either-Or Topology is T0
- Either-Or Topology is T4
- Either-Or Topology is T5
- Either-Or Topology is Topology