{\displaystyle X} and Y {\displaystyle Y} are homeomorphic. A self-homeomorphism is a homeomorphism from a topological space onto itself. Being "homeomorphic"...

action of the homeomorphism group of a space on that space. Let X {\displaystyle X} be a topological space and denote the homeomorphism group of X {\displaystyle...

homeomorphisms versus homeomorphisms Every homeomorphism is a local homeomorphism. But a local homeomorphism is a homeomorphism if and only if it is bijective...

interior. The three homeomorphisms yield a single homeomorphism of the boundary of the triangle. By the Alexander trick this homeomorphism can be extended...

{\displaystyle X\times _{Y}Y'\to Y'} is a homeomorphism of topological spaces. A morphism of schemes is a universal homeomorphism if and only if it is integral,...

closely related to the stable homeomorphism conjecture (now proved) which states that every orientation-preserving homeomorphism of Euclidean space is stable...

demonstrate. If ( X , d ) {\displaystyle (X,d)} is a metric space, a homeomorphism f : X → X {\displaystyle f\colon X\to X} is said to be expansive if...

assumed to act as homeomorphisms on X. The structure of a G-space is a group homomorphism ρ : G → Homeo(X) into the homeomorphism group of X. Similarly...

In mathematics, the y-homeomorphism, or crosscap slide, is a special type of auto-homeomorphism in non-orientable surfaces. It can be constructed by sliding...

there exists a homeomorphism h : E → E ′ {\displaystyle h:E\rightarrow E'} , such that the diagram commutes. If such a homeomorphism exists, then one...

notion of a triangulation. An isomorphism of PL manifolds is called a PL homeomorphism. PL, or more precisely PDIFF, sits between DIFF (the category of smooth...

hardness of the subgraph homeomorphism problem, see e.g. LaPaugh, Andrea S.; Rivest, Ronald L. (1980), "The subgraph homeomorphism problem", Journal of Computer...

properties these problems do rely on. From this need arises the notion of homeomorphism. The impossibility of crossing each bridge just once applies to any...

determined, up to homeomorphism, by their fundamental groups. This conjecture is false if topological manifolds and homeomorphisms are replaced by smooth...

(Reidemeister 1935) as a classification up to PL homeomorphism, but it was shown in (Brody 1960) to be a homeomorphism classification. In modern terms, lens spaces...

boundary, by some homeomorphism. This homeomorphism is called the monodromy of the surface bundle. It is possible to show that the homeomorphism type of the...

Euclidean plane E2. Such a neighborhood, together with the corresponding homeomorphism, is known as a (coordinate) chart. It is through this chart that the...

self homeomorphism acts on the closed curve along b. In the tubular neighborhood it takes the curve of b once along the curve of a. A homeomorphism between...

example of a quasiconformal homeomorphism that is not smooth. If s = 0, this is simply the identity map. A homeomorphism is 1-quasiconformal if and only...

the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform...

is (topologically) homogeneous if for every x and y in X there is a homeomorphism f : X → X {\displaystyle f\colon X\to X} such that f ( x ) = y . {\displaystyle...

(respectively, smooth manifold). Since two homeomorphisms h : U → V and g : V → W compose to a homeomorphism from U to W, one asks that the pseudogroup...

a homeomorphism, f {\displaystyle f} and its inverse need only be continuous. Every diffeomorphism is a homeomorphism, but not every homeomorphism is...

orientation-preserving homeomorphism of the circle S 1 = R / Z . {\displaystyle S^{1}=\mathbb {R} /\mathbb {Z} .} Then f may be lifted to a homeomorphism F : R → R...

several questions regarding the topology of the GSC it represents. The homeomorphism problem is: given two finite simplicial complexes representing smooth...

in R n {\displaystyle \mathbb {R} ^{n}} and f {\displaystyle f} is a homeomorphism between U {\displaystyle U} and V {\displaystyle V} . The theorem and...

homeomorphism can be used as a global chart for X . {\displaystyle X.} Thus, in the infinite-dimensional, separable, metric case, up to homeomorphism...

that φ is a homeomorphism onto its image; in the usage of some authors, this may instead mean that φ : U → Rn is itself a homeomorphism. The presence...

that are homotopy-equivalent to a point are called contractible. A homeomorphism is a special case of a homotopy equivalence, in which g ∘ f is equal...

simplicial complexes by the choice of an appropriate homeomorphism. A space that admits such a homeomorphism is called a triangulable space. Triangulations...