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Topic: Covering map

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	PlanetMath: covering space
		Covering maps are especially important in the study of Riemann surfaces; in this context, one sometimes discusses a generalized notion of covering map called a “ramified covering”; this allows one to replace a discrete set of the local homeomorphisms by maps that locally look like
		Covering maps are also generalized in algebraic geometry; there the corresponding notion is that of étale morphism.
		This is version 17 of covering space, born on 2001-11-16, modified 2005-08-08.
	www.planetmath.org /encyclopedia/CoveringMap.html (269 words)

	Aardvark Map - Free custom Google Maps in minutes
		Use the zoom ladder on the side of the map to zoom in and out by small or large amount.
		Full details about the various linking types are included in the help section, but there are options covering various possibilities from embedding the map in your site, to linking to it in an e-mail.
		The map ID changes each time you edit the map in step 1 or 2, when you return to step 3.
	www.aardvarkmap.net (2959 words)

	Catalog of USGS Map Products: Planetary
		Map sheet 1 measures at 34"x54", at a scale of 1:2,000,000, and is the first formal geologic map focused on the Olympus Mons region.
		Map sheet 2 measures at 45"x39", at a scale of 1:1,000,000 as a special-scale topographic map of the shield area of the volcano that was constructed from stereoscopic image pairs by using conventional photogrammetric techniques and analytical stereoplotters.
		Geologic Map of the Polar Regions of Mars--These geologic maps of the north and south polar regions of Mars, extend to 55 degrees north and south latitude.
	rockyweb.cr.usgs.gov /outreach/mapcatalog/planetary.html (3652 words)

	Covering space - Wikipedia, the free encyclopedia
		In mathematics, a covering space is a topological space C which "covers" another space X by a surjective local homeomorphism p : C → X called a covering map.
		Covering spaces are studied in algebraic topology, but they have important applications in many other branch of mathematics including differential topology, the theory of topological groups, and the theory of Riemann surfaces.
		The map p is called the covering map and the space X is often called the base of the covering.
	en.wikipedia.org /wiki/Covering_map (1815 words)

	[No title]
		It's clear that the map is finite-to-one everywhere, but I can (I think) visualize examples where such a map is _not_ a covering map.
		I guess that's _forced_ by the assumption that p is a covering map, since the definition of such a map says that every point in the basespace has evenly-covered neighborhoods...
		and that implies that a covering map is a surjection.
	www.math.niu.edu /~rusin/known-math/00_incoming/covering (972 words)

	Russia maps from Omni Resources, world leader in map supply.
		The cover and legend are in English, the maps are in Russian.
		A double-side map presenting the Kamchatka Peninsula (actually the Kamchatska oblast) in two halves: the northern part (from Ust-Kamchatsk to the northern border) is at the smaller scale of 1:1,200,000, the southern part is at 1:800,000.
		Covers from Helsinki and Tallinn (north and west of St. Petersburg) to Smolensk and Tula (south and east of Moscow).
	www.omnimap.com /catalog/int/russia.htm (2061 words)

	C:\html\nyspath2.htm
		Map of geological cross-section by Samuel Akerly in 1819.
		Map of the counties of Albany and Schenectady
		Map of the counties of Dutchess and Putnam
	www.sunysb.edu /libmap/nypath4.htm (6930 words)

	16th - 17th Century Maps
		Below are maps of the empire and Anatolia from the atlases of the prominent map makers and publishers of the period.
		The map covers Ottoman territories in the Balkans, Anatolia, Levant, Arabia and North Africa.
		In the main title at the bottom margin it is explained that this map was ''designed by Sanson, Geographer to the French King, and rendered into English and illustrated with figures by Richard Blome by the King's special command''.
	turkeyinmaps.com /Sayfa2.html (1351 words)

	18th - 19th Century Maps
		With regards to maps of Turkish Empire and Anatolia during this period, we begin to see the current local names of regions and cities as compared to the classical names shown in the earlier maps.
		One of the few maps that cover the whole of the Mediterranean and include the western most provinces of the Empire in North Africa.
		Map has a highly decorative fl and white title cartouche at the bottom left which seem to be a characteristic of German maps of the period.
	www.turkeyinmaps.com /Sayfa3.html (591 words)

	Wild Rose gpsMaps - Topography, Scale, Projection
		The sections on UTM and datum are especially important when using a GPS receiver with a map.
		A map covering a small area like a county or town will have a larger scale (1:24,000).
		Maps are a flat rendering of the surface of the nearly-spherical Earth.
	www.okono.com /maps.html (328 words)

	1
		A Map of the route from the city of Albany to the Fort Osswego on the Lake of Cataroque.
		Map of the roads from New Rochelle to Kingstreet, Westchester County.
		Map of the 1780 raids of the Schoharie and Mohawk valleys.
	www.sunysb.edu /libmap/nypath2.htm (6305 words)

	Malaysia maps from Omni Resources, world leader in map supply.
		The Rough Guide Map Malaysia combines clear modern mapping and up-to-date research and is the essential companion to anyone travelling around this richly diverse country.
		On one side is a small general map at 1:6.5m of the whole of Malaysia, with larger road maps of Peninsular Malaysia and Saba & Sarawak at 1:1.5m and 1:2m respectively.
		A two-sheet map covering the southern province on Kalimantan Island.
	www.omnimap.com /catalog/int/malaysia.htm (812 words)

	Humboldt State University Library -- Atlas and Map Collection
		The Atlas and Map Collection is located in the southwest corner of the first floor of the HSU Library at approximately 40° 52' 36"N, 124° 04' 49"W (WGS84/NAD83); UTM 10 408976E 4525630N (WGS84/NAD83); and in the SW 1/4 of the NW 1/4, Section 28, T6N, R1E of the Humboldt Meridian.
		Maps are arranged in cabinets using the Library of Congress Classification System which arranges maps first by geographic area, then by subject, region, or political subdivision within the geographic area.
		Many map titles are actually composed of multiple sheets that together form one "map" covering a large geographic area.
	library.humboldt.edu /infoservices/atmapcoll.htm (1655 words)

	University Calgary Library NTS Map Sheets
		These map sheets are identified by the number and letter, so that the 1:250,000 map sheet covering most of the Kananaskis is designated 82J.
		Each 1:250,000 NTS map sheet is further broken into 16 blocks that measure 1/4° (15 minutes) of latitude by 1/2° (30 minutes) of longitude.
		These map sheets are identified by the number and letter of the 1:250,000 map sheet and the further number for the smaller block.
	www.ucalgary.ca /UofC/departments/INFO/library/maps/airphotos/nts.htm (215 words)

	All Shop's Collectibles : Paper : Maps : Collect at Curioshop
		One is a map of Central Asia covering the area from Lake Aral in the North West down to Tibet in the South East, Semi Palatinsk in the North to Pundschap in India.
		One map is covering the railroad routes in Austria, Hungary, Bohemia and Galicia.
		The second map is a political map of the area down south to Turkey, Bosnia, Serbia, Bulgaria and Romania.
	www.rubylane.com /shops/curioshop/ilist/,cs=Collectibles:Paper:Maps,id=2.29.2.html (569 words)

	Map and Geography Library - Topographic Maps
		Topographic maps are used widely for applications such as hiking and camping, engineering, land conservation, etc. The feature that distinguishes a topographic map from any other type of map are contour lines that show lines of equal elevation.
		A map of scale 1:24,000 means that one inch on the map is equivalent to 24,000 inches on the ground.
		A map that accompanies a map set that shows the overall arrangment of maps in the set, showing their numbering scheme and areas of coverage.
	www.library.uiuc.edu /max/topos.shtml (1262 words)

	Topographic maps mapexpress series national state county (Site not responding. Last check: )
		he standard map series covering Alaska is the 15-minute, 1:63,360-scale (1 inch = 1mile) quadrangle series, usually having dimensions of 15 minutes in latitude and from 20 to 36 minutes of longitude.
		he features shown on 15-minute maps are generally the same as those shown on 7.5 minute maps, except that some may be generalized or omitted because of the smaller scale and consequent space restrictions.
		bout 97 percent of the 2,920 sheets covering Alaska at this scale are completed; the remaining 3 percent to be done are in the Aleutian Islands and the Bering Sea islands west of the mainland.
	www.mapexp.com /topographic/topo15info.htm (221 words)

	[No title]
		mapped to V by fU (such a V is said to be evenly covered* by f*).
		In particular, a covering map over a connected base is the same
		every x in X is a covering map, which was the claim I made.
	www.mathforum.org /kb/plaintext.jspa?messageID=248816 (617 words)

	USA Road Map, Road Map of USA, Online USA Road Map, USA Road Maps, United States Road Map, USA Road Atlas, Road Map of ...
		This folded map of all the interstate road routes across the USA, is printed on laminated paper, making the map waterproof, tear proof and ideal to take along on your American trip.
		The high quality folded map displays the Eastern and Western regions of the USA on different sides of the map, comprehensively covering expressways, principal highways and even roads under construction in the entire US, including Alaska, Hawaii, Puerto Rico and the Bahamas.
		The map also shows the major time zones, international and interstate boundaries, physical features, airports, national parks, and places of interest in the United States of America.
	www.worldmapstore.com /products/USA_Road_MapBerndtson.html (225 words)

	City of Montclair, CA - Zoning Map
		The various districts are established to serve the health, safety and general welfare of the population, to provide the social and economic advantages that result from an orderly, planned use of land resources, and to guide, control and regulate future growth and development of the City.
		Below are links to the Official Zoning Map of the City of Montclair and a zoning map covering the unincorporated area of the County of San Bernardino within Montclair's sphere of influence.
		Each map is contained in a relatively large Adobe Acrobat file, so please be patient as the files may take some time to load.
	www.ci.montclair.ca.us /depts/cd/planning/zoning_map.asp (187 words)

	Math Forum Discussions - Re: a covering map
		>S/H is also a covering space of X, with covering map
		>the map you specify above is not a covering map, and I
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.com /kb/thread.jspa?forumID=13&threadID=1350659&messageID=4592008 (215 words)

	Lake District Wallpaper Digital Photographs, Pictures and Images
		In his best-selling pictorial guides to the Lakes, Alfred Wainwright described 214 individual fells and, ever since the guides were published, many people have made climbing them all a goal.
		I have now made all seven maps available for other people to use.
		Right-click on any of the maps above and choose ‘Download Link to Disc’ (or the equivalent in your browser) to download the full size (A4) map in Adobe PDF format.
	www.lakedistrictdesktops.com /maps/ridgemaps.php (202 words)

	Covering the Map of the World -- The Half-Century Legacy of the Yalta Conference, Part 5
		Covering the Map of the World -- The Half-Century Legacy of the Yalta Conference, Part 5
		Stalin made sure that the sections of the Yalta Protocols on "Liberated Europe" and "Poland," that would be published at the end of the conference, would serve as the rhetorical cover for the Sovietization of Eastern Europe.
		Things had not gone completely according to the long-term strategy that he had laid down in 1925 for the communization of Europe, but, nonetheless, half the continent of Europe was rapidly falling into Stalin's grip.
	www.fff.org /freedom/0795b.asp (1909 words)

	Pacific Southwest Region Maps & Brochures
		Full color atlases, containing 8 ½ x 11 inch topographic quadrangle maps at 1 inch to the mile scale, are available for many of the forests in California through the National Forest Store.
		These maps are 22 x 27 inches, provide the greatest level of detail and cover only small portions of each forest.
		The maps are available over-the-counter at the Regional Office in Vallejo and from the U.S. Geological Survey.
	www.fs.fed.us /r5/maps/index.shtml (281 words)

	MultiProp by AC6LA - The Map Control Window
		The input fields on the Map Control window are separated into four distinct sections controlling the transmitting antenna, the grid of receiving antennas, the ionospheric conditions to be modeled, and the way in which the modeling results are to be presented.
		The built-in Lat/Lon maps include the entire world with the "center line" being either 120° W longitude, 0° longitude, or 120° E longitude; or a lat/lon map covering the continental United States; or a lat/lon map covering Europe and the Middle East.
		The second item concerning the maps is to specify the "output parameter" that is to be shown on each map in a set.
	www.ac6la.com /mapcontrol.html (3998 words)

	World map register - Home (Site not responding. Last check: )
		The BGS map library holds map collections covering areas all over the globe.
		In some cases this will bring up a list of the maps held relevant to your chosen area, in others another map will be displayed to enable you to select a more precise location.
		Such enquiries should be directed to the organisation responsible for the map or a map supplier such as GEOPUBS or GEOCENTER.
	www.bgs.ac.uk /reference/worldmaps/worldvt.html (205 words)

	MTTA - Backcountry Huts & Trails at Rainier - Map
		The map is made of modern weatherproof and tear-proof material.
		This map can be purchased for ~$8 at local REI stores, at Whittaker Mountaineering in Ashford, or on-line at Whittaker Mountaineering MTTA Map.
		The map is being sold at the MTTA Office for the cost of $7.00 which includes sales tax.
	www.skimtta.com /map.htm (425 words)

	HCLS/OntologyTaskForce/OntologyCovering - ESW Wiki
		One alternative to building upper ontologies (UO) first, is to consider constructing a "Covering Map" between apparent overlapping sets of "related" ontologies, which can serve as a guide for an UO at a later date.
		That is, parts of A map into a region U of X where B also maps into: parts of A and B both coincide in U. However, not everything in A maps with B, or vise versa ; they only partially overlap in the covering.
		To help illustrate this, if BioPax defines protein and Uniprot does so as well, then there is the possibility of (the community) agreeing to have a Covering Map for both of them, let's call it Bio-Cover (BC), that aligns both definitions of "proteins" onto the same covering point.
	esw.w3.org /topic/HCLS/OntologyTaskForce/OntologyCovering (317 words)

	USGS Astrogeology: Planetary Map Listing
		Feature names that were not approved by the IAU General Assembly at the time a map was printed will probably not appear on that map.
		Additionally, map coordinate referencing has changed over the years as knowledge about the planetary bodies and technology have improved, and map extents recorded in our database may no longer be accurate according to current IAU coordinate reference standards.
		The number of features and maps covering those features will be reported at the bottom of the search results table.
	astrogeology.usgs.gov /Projects/MapBook/featureNameSearch_help.html (631 words)

	Great Basin National Park - Maps (U.S. National Park Service) (Site not responding. Last check: )
		The Windy Peak map covers a number of the most popular trails and well-developed trails.
		The Lehman Caves map covers mostly low-elevation areas outside the park.
		A single-sheet map covering all six topographic map areas at a scale of 1:48,000 is also available.
	www.nps.gov /grba/pphtml/maps.html (222 words)

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