Quotient space (linear algebra)In linear algebra, the quotient of a vector space by a subspace is a vector space obtained by "collapsing" to zero. The space obtained is called a quotient space and is denoted (read " mod " or " by "). Formally, the construction is as follows. Let be a vector space over a field , and let be a subspace of . We define an equivalence relation on by stating that if . That is, is related to if one can be obtained from the other by adding an element of .
Locally simply connected spaceIn mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally path-connected and locally connected. The circle is an example of a locally simply connected space which is not simply connected. The Hawaiian earring is a space which is neither locally simply connected nor simply connected. The cone on the Hawaiian earring is contractible and therefore simply connected, but still not locally simply connected.
Operator overloadingIn computer programming, operator overloading, sometimes termed operator ad hoc polymorphism, is a specific case of polymorphism, where different operators have different implementations depending on their arguments. Operator overloading is generally defined by a programming language, a programmer, or both. Operator overloading is syntactic sugar, and is used because it allows programming using notation nearer to the target domain and allows user-defined types a similar level of syntactic support as types built into a language.
Algebraic geometry and analytic geometryIn mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these subjects has numerous applications in which algebraic techniques are applied to analytic spaces and analytic techniques to algebraic varieties.
FallacyA fallacy, also known as paralogia in modern psychology, is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis. Fallacies may be committed intentionally to manipulate or persuade by deception, unintentionally because of human limitations such as carelessness, cognitive or social biases and ignorance, or potentially due to the limitations of language and understanding of language.
Straw manA straw man fallacy (sometimes written as strawman) is the informal fallacy of refuting an argument different from the one actually under discussion, while not recognizing or acknowledging the distinction. One who engages in this fallacy is said to be "attacking a straw man". The typical straw man argument creates the illusion of having refuted or defeated an opponent's proposition through the covert replacement of it with a different proposition (i.e.
