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The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

A cross-handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in the ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

The Cartesian product of a countable infinity of copies of the interval [0,1]. It can be denoted [0,1]^(aleph_0) or [0,1]^omega, where aleph_0 and omega are the first ...

A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...

A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...