On the injectivity of C1 maps of the real plane

Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Washington, D.C. and vicinity, 1862 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Topographical map of the original District of Columbia and environs showing the fortifications around the city of Washington, by E.G. Arnold C.E. It was published by G. Woolworth Colton in 1862. Scale [ca. 1:31,680]. Covers also adjacent portions of Virginia and Maryland. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Maryland State Plane Coordinate System Meters NAD83 (Fipszone 1900). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, bridges, canals, drainage, cities and towns, forts, selected public buildings and places of interest, hospitals, schools, Washington, D.C. school districts, selected private residences with names of landowners, and more. Relief is shown by hachures. Includes text and population tables. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Chemical emergency preparedness and prevention technical assistance bulletin : New York, New York : El Paso County, Colorado : Alexandria, Virginia : State of Maine.

"March 1990."

1972-1982 National Sickle Cell Disease Program, Howard University Center for Sickle Cell Disease, September 1982, Hyatt Regency-Crystal City, Arlington, Virginia.

Mode of access: Internet.

Report on the Movrico land company's coal property in Las Animas county, Colorado /

Mode of access: Internet.

Proceedings, Second International Conference on Fixed-Film Biological Processes, July 10-12, 1984, Arlington, Virginia /

"EPA/600/9-85/024a."

Jefferson's Albemarle, a guide to Albemarle County and the city of Charlottesville, Virginia.

Bibliography: p. 144-147.

History of Clarke County, Virginia and its connection with the War Between the States, with illustrations of colonial homes and of Confederate officers.

Mode of access: Internet.

Abstracts Lancaster County, Virginia, wills 1653-1800.

Mode of access: Internet.