#### 9 Citations

Hyperspaces and the S-equivariant Complete Invariance Property

- Mathematics
- 2015

In this paper it is investigated as to when a nonempty invariant closed subset A of a -space X containing the set of stationary points (S) can be the fixed point set of an equivariant continuous… Expand

On uniform flow

- Mathematics
- 2013

We obtain a condition under which a uniform flow is induced over a metric space homeomorphic to a given metric space with a uniform flow. Various examples of uniform flow are also constructed.… Expand

WAVELETS AND THE COMPLETE INVARIANCE PROPERTY

- Mathematics
- 2010

In this paper, we obtain that the space W of orthonormal wavelets enjoys the complete invariance property with respect to homeomorphisms. Further, it is obtained that the cylinder, the cone and the… Expand

COMPACT GROUPS AND FIXED POINT SETS

- Mathematics
- 1997

Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It is… Expand

The theory of continua

- Mathematics
- 1994

This survey is devoted to divisions of the theory of continua associated with snake- like, tree- like, and circlelike bicompacta, homogeneous spaces, hyperspaces of continua, and Whitney maps.

#### References

SHOWING 1-8 OF 8 REFERENCES

Fixed point sets of $1$-dimensional Peano continua.

- Mathematics
- 1980

It is shown that every nonempty closed subset of a 1dimensional Peano continuum X is the fixed point set of some continuous self-mapping of X.

Schauder bases and fixed points of nonexpansive mappings.

- Mathematics
- 1982

1* Introduction* Suppose X and Y are isomorphic Banach spaces with h\\ -\\γ || | | x &|| ||F, where || ||F and || | | x denote the norms in Y and X respectively. Let t = kh~ (this notation will be… Expand

Fixed point sets of Peano continua.

- Mathematics
- 1978

1* Introduction* A subset A of a topological space X is called a fixed point set of X if there is a (continuous) map /: X—>X such that f(x) = x iff x 6 A. If X is Hausdorff, then A is closed, and,… Expand

Fixed point sets of homeomorphisms of compact surfaces

- Mathematics
- 1971

Every closed and non-empty subset of a compact surfaceS can be the fixed point set of a homeomorphism, andS also admits fixed point free homeomorphisms if it does not have the fixed point property. A… Expand