# Category:Either-Or Topology

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This category contains results about Either-Or Topology.

Let $S = \closedint {-1} 1$ be the closed interval on the real number line from $-1$ to $1$.

Let $\tau \subseteq \powerset S$ be a subset of the power set of $S$ such that, for any $H \subseteq S$:

- $H \in \tau \iff \paren {\set 0 \nsubseteq H \lor \openint {-1} 1 \subseteq H}$

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

Then $\tau$ is the **either-or topology**, and $T = \struct {S, \tau}$ is the **either-or space**

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### E

## Pages in category "Either-Or Topology"

The following 19 pages are in this category, out of 19 total.

### E

- Either-Or Topology is Compact
- 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