Sentences with HOMEOMORPH

"A homeomorph is a mathematical term used to describe two shapes or figures that can be transformed into each other by stretching, compressing, bending, or twisting, but not tearing or cutting."

"The circle and the ellipse are homeomorphs because they can be transformed into each other through stretching."

"A torus and a coffee mug are homeomorphs since they can both be transformed into each other without tearing or cutting."

"The homeomorph of a square is a rectangle because both shapes can be transformed into each other by stretching or compressing."

"In graph theory, a homeomorph is a deformation of a graph, preserving the number of edges and vertices."

"The concept of homeomorphs is crucial in understanding the topological equivalence of different spaces."

"A homeomorph is an isomorphism in the category of topological spaces."

"The homeomorph of a closed interval is an open interval because both intervals can be transformed into each other through stretching."

"A homeomorph can change the location of its parts, but the overall shape remains the same."

"In algebraic topology, homeomorphs are used to define the concept of a fundamental group."

"A homeomorph of a cube is a tetrahedron because both have the same number of edges and vertices."

"The concept of homeomorphs is closely related to the idea of continuous transformations."

"A homeomorph can be thought of as a continuous stretching or bending of a shape."

"The homeomorph of a line segment is the real line because both have infinitely many points and can be transformed into each other."

"In topology, homeomorphs are used to define the concept of homeomorphism."

"A homeomorph can be visualized as a rubber band that can be stretched or twisted without breaking."