vacuous
Suppose $X$ is a set and $P$ is a property defined as follows:
$X$ has property $P$ if and only if  
$\forall Y[$ $Y$ satisfies condition $1]\Rightarrow $ $Y$ satisfies condition $2$ 
where condition $1$ and condition $2$ define the property. If condition $1$ is never satisfied then $X$ satisfies property $P$ vacuously.
Examples

1.
If $X$ is the set $\{1,2,3\}$ and $P$ is the property defined as above with condition $1=$ $Y$ is a infinite subset of $X$, and condition $2=$ $Y$ contains $7$. Then $X$ has property $P$ vacously; every infinite subset of $\{1,2,3\}$ contains the number $7$ [1].

2.
The empty set^{} is a Hausdorff space (vacuously).

3.
Suppose property $P$ is defined by the statement :
The present King of France does not exist.
Then either of the following propositions^{} is satisfied vacuously.
The present king of France is bald.
The present King of France is not bald.
References
 1 Wikipedia http://en.wikipedia.org/wiki/Vacuous_truthentry on Vacuous truth.
Title  vacuous 

Canonical name  Vacuous 
Date of creation  20130322 14:42:27 
Last modified on  20130322 14:42:27 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  9 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 00A20 
Synonym  vacuously 
Synonym  vacuously true 
Synonym  vacuous truth 