**SPHERE INTERSECTIONS IN E**

^{n}(n≥1)**K**=

**H**(P

_{1},a

_{1}) ∩

**H**(P

_{2},a

_{2}) ∩ ... ∩

**H**(P

_{n},a

_{n})

where

a

_{i}≥ a

_{i+1}> 0 for i = 1, 2, ... , n-1.

and

P

_{1}∈

**E**and

^{n}P

_{i}∈

**H**(P

_{1},a

_{1}) ∩

**H**(P

_{2},a

_{2}) ∩ ... ∩

**H**(P

_{i-1},a

_{i-1})

for i = 2, 3, ... , n.

**DEFINITIONS**

•

**E**denotes Euclidean n-space. The set of n-tuples of

^{n}real numbers.

• If P ∈

**E**and r is a real number greater than zero, then

^{n}**H**(P,r) = { Q ∈

**E**(P,Q) = r }.

^{n}| δA "sphere" with center P and radius r.

•

**δ**(P,Q) denotes the distance between points P and Q in

**E**.

^{n}**QUESTION**

Is

**K**empty ?