# Fixed point sets of homeomorphisms of metric products

@inproceedings{Martin1988FixedPS,
title={Fixed point sets of homeomorphisms of metric products},
author={John R. Martin},
year={1988}
}
In this paper it is investigated as to when a nonempty closed subset A of a metric product X containing intervals or spheres as factors can be the fixed point set of an autohomeomorphism of X. It is shown that if X is the Hilbert cube Q or contains either the real line R or a (2n 1)-sphere S2n-1 as a factor, then A can be any nonempty closed subset. In the case where A is in Int(Bf2n+1), the interior of the closed unit (2n + 1)-ball B2n+l, a strong necessary condition is given. In particular… Expand
Fixed point sets of Tychonov cubes
• Mathematics
• 1995
Abstract We give a spectral characterization of the compacta (compact Hausdorff spaces) which admit embeddings into uncountable products of the closed unit interval such that the embedded imagesExpand
G-spaces and Fixed Point Sets
• Mathematics
• 2000
For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact groupExpand
Hyperspaces and the S-equivariant Complete Invariance Property
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 continuousExpand
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 isExpand
Fixed point sets of autohomeomorphisms of uncountable products
• Mathematics
• 1997
Abstract It is shown that every nonempty closed subset of any uncountable power of a metrizable compact group (or the real line or the irrationals) is the fixed point set an autohomeomorphism of thatExpand
Topology Proceedings 39 (2012) pp. 185-194: Topological Left-loops
In this note we define the concept of a topological leftloop which generalizes the notion of a topological loop, and we show that it is a useful tool in unifying arguments on traditional spaces of aExpand
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 theExpand
On uniform flow
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
Complete Invariance Property with respect to Homeomorphism over Frame Multiwavelet and Super-Wavelet Spaces
We discuss the complete invariance property with respect to homeomorphism (CIPH) over various sets of wavelets containing all orthonormal multiwavelets, all tight frame multiwavelets, allExpand

#### References

SHOWING 1-9 OF 9 REFERENCES
On fixed point sets of homeomorphisms of then-ball
Conditions are investigated under which a subsetA can be the fixed point set of a homeomorphism ofBn. If eitherA ∩ ∂Bn ≠ Ø andn arbitrary orA ∩ ∂Bn=Ø andn even it is necessary and sufficient thatA isExpand
Fixed point sets of homeomorphisms of compact surfaces
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. AExpand
Lectures on Hilbert Cube Manifolds
Preliminaries Z-sets in Q Stability of Q-manifoldsitle> Z-sets in Q-manifolds Q-manifolds of the form $M \times [0, 1)$ Shapes of Z-sets in Q Near homeomorphisms and the Sum Theorem Applications ofExpand
Algebraic Topology: An Introduction
Professor Massey's book developed from lecture notes of courses taught to Yale undergraduate and graduate students over a period of several years, and is the author of numerous research articles on algebraic topology and related topics. Expand
Fixed point sets of metric and nonmetric spaces
• Mathematics
• 1984
Introduction to Knot Theory
• Mathematics
• 1977
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9173473715782166, "perplexity": 975.3757656851461}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057403.84/warc/CC-MAIN-20210922223752-20210923013752-00477.warc.gz"}