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Robert Sorgenfrey
Robert Henry Sorgenfrey (August 14, 1915 – January 7, 1996) was an American mathematician and Professor Emeritus of Mathematics at the University of California, Los Angeles. The Sorgenfrey line and the Sorgenfrey plane are named after him; the Sorgenfrey line was the first example of a normal topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ... whose product with itself is not normal. References 1915 births 1996 deaths 20th-century American mathematicians {{US-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunbury, Iowa
Sunbury is an unincorporated community in Cedar County, Iowa, United States. It is located just west of the intersection of County Roads F44 and Y26, in the southeastern part of the county, southeast of Bennett and north of Durant Durant may refer to: People * Durant (surname) Fictional characters * Durant (Pokémon), a species in ''Pokémon Black'' and ''White'' * ''John Durant'' (General Hospital), a character on the soap opera ''General Hospital'' Places * Durant, ..., at 41.669882N, -90.928795W). The population is estimated to be 50 persons.Wundram, Bill (2010-11-29)"The 'last dance' at a 115-year-old hall" ''Quad City Times''. Retrieved 2011-04-24. History Sunbury was founded when the railroad was introduced into the area. Sunbury's population was 13 in 1902, and 107 in 1925. Sunbury was the location of the Sunbury Dance Hall, which opened ''circa'' 1895 and closed in 1964. The hamlet also boasted a bank, which opened in 1901.Aurner, C.R. (1910). ''A topical history ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles, California
Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the world's most populous megacities. Los Angeles is the commercial, financial, and cultural center of Southern California. With a population of roughly 3.9 million residents within the city limits , Los Angeles is known for its Mediterranean climate, ethnic and cultural diversity, being the home of the Hollywood film industry, and its sprawling metropolitan area. The city of Los Angeles lies in a basin in Southern California adjacent to the Pacific Ocean in the west and extending through the Santa Monica Mountains and north into the San Fernando Valley, with the city bordering the San Gabriel Valley to it's east. It covers about , and is the county seat of Los Angeles County, which is the most populous county in the United States with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five major unincorporated territories, nine United States Minor Outlying Islands, Minor Outlying Islands, and 326 Indian reservations. The United States is also in Compact of Free Association, free association with three Oceania, Pacific Island Sovereign state, sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Palau, Republic of Palau. It is the world's List of countries and dependencies by area, third-largest country by both land and total area. It shares land borders Canada–United States border, with Canada to its north and Mexico–United States border, with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the List of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. The fundamental concepts in point-set topology are ''continuity'', ''compactness'', and ''connectedness'': * Continuous functions, intuitively, take nearby points to nearby points. * Compact sets are those that can be covered by finitely many sets of arbitrarily small size. * Connected sets are sets that cannot be divided into two pieces that are far apart. The terms 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using the concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Los Angeles
The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a Normal school, teachers college then known as the southern branch of the California State Normal School (now San Jose State University, San José State University). This school was absorbed with the official founding of UCLA as the Southern Branch of the University of California in 1919, making it the second-oldest of the 10-campus University of California system (after UC Berkeley). UCLA offers 337 undergraduate and graduate degree programs in a wide range of disciplines, enrolling about 31,600 undergraduate and 14,300 graduate and professional students. UCLA received 174,914 undergraduate applications for Fall 2022, including transfers, making the school the most applied-to Higher education in the United States, university in the United States. The university is or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Texas At Austin
The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 graduate students and 3,133 teaching faculty as of Fall 2021, it is also the largest institution in the system. It is ranked among the top universities in the world by major college and university rankings, and admission to its programs is considered highly selective. UT Austin is considered one of the United States's Public Ivies. The university is a major center for academic research, with research expenditures totaling $679.8 million for fiscal year 2018. It joined the Association of American Universities in 1929. The university houses seven museums and seventeen libraries, including the LBJ Presidential Library and the Blanton Museum of Art, and operates various auxiliary research facilities, such as the J. J. Pickle Researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorgenfrey Line
In mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set \mathbb of real numbers; it is different from the standard topology on \mathbb (generated by the open intervals) and has a number of interesting properties. It is the topology generated by the basis of all half-open intervals ''a'',''b''), where ''a'' and ''b'' are real numbers. The resulting /nowiki>''a'',''b''), where ''a'' and ''b'' are real numbers. The resulting topological space is called the Sorgenfrey line after Robert Sorgenfrey">topological space">/nowiki>''a'',''b''), where ''a'' and ''b'' are real numbers. The resulting topological space is called the Sorgenfrey line after Robert Sorgenfrey or the arrow and is sometimes written \mathbb_l. Like the Cantor set and the long line (topology), long line, the Sorgenfrey line often serves as a useful counterexample to many otherwise plausible-sounding conjectures in general topology. The product space, produc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorgenfrey Plane
In topology, the Sorgenfrey plane is a frequently-cited counterexample to many otherwise plausible-sounding conjectures. It consists of the product of two copies of the Sorgenfrey line, which is the real line \mathbb under the half-open interval topology. The Sorgenfrey line and plane are named for the American mathematician Robert Sorgenfrey. A basis for the Sorgenfrey plane, denoted \mathbb from now on, is therefore the set of rectangles that include the west edge, southwest corner, and south edge, and omit the southeast corner, east edge, northeast corner, north edge, and northwest corner. Open sets in \mathbb are unions of such rectangles. \mathbb is an example of a space that is a product of Lindelöf spaces that is not itself a Lindelöf space. The so-called anti-diagonal \Delta = \ is an uncountable discrete subset of this space, and this is a non- separable subset of the separable space \mathbb. It shows that separability does not inherit to closed subspaces. Note ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Space
In topology and related branches of mathematics, a normal space is a topological space ''X'' that satisfies Axiom T4: every two disjoint closed sets of ''X'' have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces. Definitions A topological space ''X'' is a normal space if, given any disjoint closed sets ''E'' and ''F'', there are neighbourhoods ''U'' of ''E'' and ''V'' of ''F'' that are also disjoint. More intuitively, this condition says that ''E'' and ''F'' can be separated by neighbourhoods. A T4 space is a T1 space ''X'' that is normal; this is equivalent to ''X'' being normal and Hausdorff. A completely normal space, or , is a topological space ''X'' such that every subspace of ''X'' with subspace topology is a normal space. It turns out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1915 Births
Events Below, the events of World War I have the "WWI" prefix. January *January – British physicist Sir Joseph Larmor publishes his observations on "The Influence of Local Atmospheric Cooling on Astronomical Refraction". * January 1 ** WWI: British Royal Navy battleship HMS ''Formidable'' is sunk off Lyme Regis, Dorset, England, by an Imperial German Navy U-boat, with the loss of 547 crew. ** Battle of Broken Hill: A train ambush near Broken Hill, New South Wales, Australia, is carried out by two men (claiming to be in support of the Ottoman Empire) who are killed, together with 4 civilians. * January 5 – Joseph E. Carberry sets an altitude record of , carrying Capt. Benjamin Delahauf Foulois as a passenger, in a fixed-wing aircraft. * January 12 ** The United States House of Representatives rejects a proposal to give women the right to vote. ** ''A Fool There Was'' premières in the United States, starring Theda Bara as a ''femme fatale''; she quickly b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
