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A tilde over an equals sign, or a plain tilde, between two spaces.
Also known as: Homeomorphic sign, Topologically equivalent sign, Homeomorphism symbol
Two spaces are homeomorphic if one can be deformed into the other without cutting or gluing, and the sign says so. It is weaker than equality and stronger than mere similarity of shape, and it is what makes a coffee cup and a doughnut the same object.
States that two topological spaces are homeomorphic — related by a continuous bijection with continuous inverse.
Contexts: Mathematics
Is written ≅ or ≈ depending on the text, both of which are also used for other equivalences; topology texts declare their convention.
Contexts: Mathematics
A horizontal wavy stroke set directly above one or two horizontal straight strokes.