Question: Information: - In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R (in topology, a circle isn't bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself. - In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions. - In the mathematical subject of topology, an ambient isotopy, also called an "h-isotopy", is a kind of continuous distortion of an "ambient space", a manifold, taking a submanifold to another submanifold. For example in knot theory, one considers two knots the same if one can distort one knot into the other without breaking it. Such a distortion is an example of an ambient isotopy. More precisely, let "N" and "M" be manifolds and "g" and "h" be embeddings of "N" in "M". A continuous map is defined to be an ambient isotopy taking "g" to "h" if "F" is the identity map, each map "F" is a homeomorphism from "M" to itself, and "F" "g" = "h". This implies that the orientation must be preserved by ambient isotopies. For example, two knots which are mirror images of each other are in general not equivalent. - The State University of New York at Buffalo is a public research university with campuses in Buffalo and Amherst, New York, United States. It is commonly referred to as the University at Buffalo (UB) or SUNY Buffalo, and it was formerly known as the University of Buffalo. The university was founded in 1846 as a private college, but in 1962 merged with the State University of New York (SUNY) system. By enrollment, UB is the largest in the SUNY system, and also the largest public university in the northeastern United States (consisting of New York state and the New England region). UB also has the largest endowment and research funding, as a comprehensive university center in the SUNY system. - In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. - In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. - A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. - William W. Menasco is a topologist and a professor at the University at Buffalo . He is best known for his work in knot theory . - The State University of New York (SUNY ) is a system of public institutions of higher education in New York, United States. It is one of the largest comprehensive systems of universities, colleges, and community colleges in the United States, with a total enrollment of 465,000 students, plus 1.1 million adult education students, spanning 64 campuses across the state. Led by Chancellor Nancy L. Zimpher, the SUNY system has 88,000 faculty members and some 7,660 degree and certificate programs overall and a $10.7 billion budget. SUNY includes many institutions and four University Centers: Albany (1844), Buffalo (1846), Binghamton (1946), and Stony Brook (1957). SUNY's administrative offices are in Albany, the state's capital, with satellite offices in Manhattan and Washington, D.C. SUNY's largest campus is the University at Buffalo, which also has the greatest endowment and research funding. - In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spacesthat is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word "homeomorphism" comes from the Greek words "" ("homoios") = similar and "" ("morph") = shape, form. - A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. - In mathematics, topology (from the Greek , "place", and , "study") is concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important topological properties include connectedness and compactness. What object entity has the relation of 'field of work' with the subject 'william menasco'? Choices: - education - geometry - knot theory - language - mathematics - physics - research - topology - track - training
Answer: topology

Question: Information: - Innsbruck is the capital city of Tyrol in western Austria. It is located in the Inn valley, at its junction with the Wipp valley, which provides access to the Brenner Pass some to the south. - Imst is a town in the Austrian federal state of Tyrol. It lies on the River Inn in western Tyrol, some west of Innsbruck and at an altitude of above sea level. With a current population (2013) of 9,552, Imst is the administrative centre of Imst District. - Haiming is a municipality in the district of Imst in the Austrian state of Tyrol . What object entity has the relation of 'located in the administrative territorial entity' with the subject 'haiming'? Choices: - austria - brenner - centre - district - imst district - innsbruck - of - river
Answer:
imst district