# Category:Double Pointed Topologies

Jump to navigation
Jump to search

This category contains results about Double Pointed Topologies.

Definitions specific to this category can be found in Definitions/Double Pointed Topologies.

Let $T = \struct {S, \tau_S}$ be a topological space.

Let $A = \set {a, b}$ be a doubleton.

Let $D = \struct {A, \set {\O, A} }$ be the indiscrete space on $A$.

Let $\struct {T \times D, \tau}$ be the product space of $T$ and $D$.

Then $T \times D$ is known as the **double pointed topology** on $T$.

## Subcategories

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

## Pages in category "Double Pointed Topologies"

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

### C

### D

- Double Pointed Countable Complement Topology fulfils no Separation Axioms
- Double Pointed Countable Complement Topology is Weakly Countably Compact
- Double Pointed Discrete Real Number Space is not Lindelöf
- Double Pointed Discrete Real Number Space is Weakly Countably Compact
- Double Pointed Finite Complement Topology fulfils no Separation Axioms
- Double Pointed Finite Complement Topology is Compact
- Double Pointed Fortissimo Space is Lindelöf
- Double Pointed Fortissimo Space is not Pseudocompact
- Double Pointed Fortissimo Space is not Sigma-Compact
- Double Pointed Fortissimo Space is Weakly Countably Compact
- Double Pointed Topology is not T0