2-sided and 3-manifold

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Difference between 2-sided and 3-manifold

2-sided vs. 3-manifold

In topology, a compact codimension one submanifold F of a manifold M is said to be 2-sided in M when there is an embedding with h(x,0). In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

Codimension

In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

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Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

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Embedding

In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

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Fundamental group

In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Submanifold

In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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