Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
Privacy lawPrivacy law is the body of law that deals with the regulating, storing, and using of personally identifiable information, personal healthcare information, and financial information of individuals, which can be collected by governments, public or private organisations, or other individuals. It also applies in the commercial sector to things like trade secrets and the liability that directors, officers, and employees have when handing sensitive information.
Collective intelligenceCollective intelligence (CI) is shared or group intelligence (GI) that emerges from the collaboration, collective efforts, and competition of many individuals and appears in consensus decision making. The term appears in sociobiology, political science and in context of mass peer review and crowdsourcing applications. It may involve consensus, social capital and formalisms such as voting systems, social media and other means of quantifying mass activity.
Right to privacyThe right to privacy is an element of various legal traditions that intends to restrain governmental and private actions that threaten the privacy of individuals. Over 150 national constitutions mention the right to privacy. On 10 December 1948, the United Nations General Assembly adopted the Universal Declaration of Human Rights (UDHR), originally written to guarantee individual rights of everyone everywhere; while right to privacy does not appear in the document, many interpret this through Article 12, which states: "No one shall be subjected to arbitrary interference with his privacy, family, home or correspondence, nor to attacks upon his honour and reputation.
Standard basisIn mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction.
Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
PrivacyPrivacy (UK, US) is the ability of an individual or group to seclude themselves or information about themselves, and thereby express themselves selectively. The domain of privacy partially overlaps with security, which can include the concepts of appropriate use and protection of information. Privacy may also take the form of bodily integrity. There have been many different conceptions of privacy throughout history. Most cultures recognize the right of an individual to withhold aspects of their personal lives from public record.
Paracompact spaceIn mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions of unity subordinate to any open cover. Sometimes paracompact spaces are defined so as to always be Hausdorff. Every closed subspace of a paracompact space is paracompact.
Alternative educationAlternative education encompasses many pedagogical approaches differing from mainstream pedagogy. Such alternative learning environments may be found within state, charter, and independent schools as well as home-based learning environments. Many educational alternatives emphasize small class sizes, close relationships between students and teachers and a sense of community. The legal framework for such education varies by locality, and determines any obligation to conform with mainstream standard tests and grades.
Fundamental groupIn the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger case of homeomorphic) have isomorphic fundamental groups.
