As a consequence of Theorem 1 of this paper, we see that if X and Y are globally 1-alg continua in
S
n
(
n
⩾
5
)
{S^n}\;(n \geqslant 5)
having the shape of the real projective space
P
k
(
k
≠
2
,
2
k
+
2
⩽
n
)
{P^k}\;(k \ne 2,2k + 2 \leqslant n)
, then
S
n
−
X
≈
S
n
−
Y
{S^n} - X \approx {S^n} - Y
. (For
P
1
=
S
1
{P^1} = {S^1}
, this establishes the last case of such a result for spheres.) We also show that if X and Y are globally 1-alg continua in
S
n
,
n
⩾
6
{S^n},n \geqslant 6
, which have the shape of a codimension
⩾
3
\geqslant 3
, closed,
0
>
(
2
m
−
n
+
1
)
0 > (2m - n + 1)
-connected, PL-manifold
M
m
{M^m}
, then
S
n
−
X
≈
S
n
−
Y
{S^n} - X \approx {S^n} - Y
.