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  2. Boundary (topology) - Wikipedia

    en.wikipedia.org/wiki/Boundary_(topology)

    In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

  3. DE-9IM - Wikipedia

    en.wikipedia.org/wiki/DE-9IM

    where ⁠ ⁠ is the dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.. The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its ...

  4. Dehn surgery - Wikipedia

    en.wikipedia.org/wiki/Dehn_surgery

    In order to describe a Dehn surgery, [1] one picks two oriented simple closed curves and on the corresponding boundary torus of the drilled 3-manifold, where is a meridian of (a curve staying in a small ball in and having linking number +1 with or, equivalently, a curve that bounds a disc that intersects once the component ) and is a longitude ...

  5. List of general topology topics - Wikipedia

    en.wikipedia.org/wiki/List_of_general_topology...

    Continuum (topology) Extended real number line; Long line (topology) Sierpinski space; Cantor set, Cantor space, Cantor cube; Space-filling curve; Topologist's sine curve; Uniform norm; Weak topology; Strong topology; Hilbert cube; Lower limit topology; Sorgenfrey plane; Real tree; Compact-open topology; Zariski topology; Kuratowski closure ...

  6. Chain (algebraic topology) - Wikipedia

    en.wikipedia.org/wiki/Chain_(algebraic_topology)

    A chain that is the boundary of another chain is called a boundary. Boundaries are cycles, so chains form a chain complex, whose homology groups (cycles modulo boundaries) are called simplicial homology groups. Example 3: The plane punctured at the origin has nontrivial 1-homology group since the unit circle is a cycle, but not a boundary.

  7. Homotopical connectivity - Wikipedia

    en.wikipedia.org/wiki/Homotopical_connectivity

    A 2-dimensional hole (a hole with a 1-dimensional boundary). A 2-dimensional hole (a hole with a 1-dimensional boundary) is a circle (S 1) in X, that cannot be shrunk continuously to a point in X. An example is shown on the figure at the right. The yellow region is the topological space X; it is a pentagon with a triangle removed.

  8. Surface (topology) - Wikipedia

    en.wikipedia.org/wiki/Surface_(topology)

    An open surface with x-, y-, and z-contours shown.. In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball.

  9. List of topologies - Wikipedia

    en.wikipedia.org/wiki/List_of_topologies

    The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.