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  2. Hegewisch, Chicago - Wikipedia

    en.wikipedia.org/wiki/Hegewisch,_Chicago

    Hegewisch (pronounced / ˈ h ɛ ɡ ˌ w ɪ ʃ / "heg-wish" by the locals) is one of the 77 community areas of Chicago, Illinois, located on the city's far south side.It is bordered by the neighborhoods of Riverdale and South Deering to the west, the East Side to the north, the village of Burnham to the south and the city of Hammond, Indiana to the east.

  3. Neighborhoods of Alexandria, Virginia - Wikipedia

    en.wikipedia.org/wiki/Neighborhoods_of...

    Neighborhoods of Alexandria, Virginia. Alexandria, Virginia is an independent city in the Commonwealth of Virginia, located along the western bank of the Potomac River. The city of approximately 151,000 is about six miles (9.6 kilometers) south of downtown Washington, D.C.

  4. West Pullman, Chicago - Wikipedia

    en.wikipedia.org/wiki/West_Pullman,_Chicago

    West Pullman is a neighborhood located on the far south side of the city of Chicago, Illinois. It is one of the 77 official community areas of Chicago. The neighborhood was initially inhabited by workers of the Pullman Train Company looking to escape the grip of the company town, but soon swelled with industrial workers of all stripes. The ...

  5. Hyde Park, Chicago - Wikipedia

    en.wikipedia.org/wiki/Hyde_Park,_Chicago

    Hyde Park is a neighborhood on the South Side of Chicago, Illinois, located on and near the shore of Lake Michigan 7 miles (11 km) south of the Loop. It is one of the city's 77 municipally recognized community areas. Hyde Park's boundaries and subdivisions have several local definitions. The community area's formal boundaries are 51st Street ...

  6. Hausdorff space - Wikipedia

    en.wikipedia.org/wiki/Hausdorff_space

    In topology and related branches of mathematics, a Hausdorff space (/ ˈhaʊsdɔːrf / HOWSS-dorf, / ˈhaʊzdɔːrf / HOWZ-dorf[1]), T2 space or separated space, is a topological space where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T 2) is ...

  7. Neighbourhood system - Wikipedia

    en.wikipedia.org/wiki/Neighbourhood_system

    Said differently, is a neighborhood of a point if and only if. Neighbourhood bases. In any topological space, the neighbourhood system for a point is also a neighbourhood basis for the point. The set of all open neighbourhoods at a point forms a neighbourhood basis at that point. For any point in a metric space, the sequence of open balls ...

  8. Derivative of the exponential map - Wikipedia

    en.wikipedia.org/wiki/Derivative_of_the...

    The derivative of the exponential map is given by [6] (1) Explanation. X = X(t) is a C1 (continuously differentiable) path in the Lie algebra with derivative X′ (t) = ⁠dX (t) / dt⁠. The argument t is omitted where not needed. adX is the linear transformation of the Lie algebra given by adX(Y) = [X, Y]. It is the adjoint action of a Lie ...

  9. Locally compact space - Wikipedia

    en.wikipedia.org/wiki/Locally_compact_space

    The right order topology on the real line is locally compact in senses (1) and (3) but not in senses (2) or (4), because the closure of any neighborhood is the entire non-compact space. The Sierpiński space is locally compact in senses (1), (2) and (3), and compact as well, but it is not Hausdorff or regular (or even preregular) so it is not ...