With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: American Broadcasting Company was bought by Citadel Broadcasting.
text_B: In mathematics , a pointed set -LRB- also based set or rooted set -RRB- is an ordered pair where is a set and is an element of called the base point , also spelled basepoint .. mathematics. mathematics. ordered pair. ordered pair. set. Set ( mathematics ). Maps between pointed sets and -LRB- called based maps , pointed maps , or point-preserving maps -RRB- are functions from to that map one basepoint to another , i.e. a map such that .. functions. function ( mathematics ). This is usually denoted. Pointed sets may be regarded as a rather simple algebraic structure .. algebraic structure. algebraic structure. In the sense of universal algebra , they are structures with a single nullary operation which picks out the basepoint .. universal algebra. universal algebra. nullary operation. nullary operation. The class of all pointed sets together with the class of all based maps form a category .. class. Class ( set theory ). category. category theory. In this category the pointed singleton set is an initial object and a terminal object , i.e. a zero object .. set. Set ( mathematics ). category. category theory. singleton set. singleton set. initial object. initial object. terminal object. terminal object. zero object. zero object. There is a faithful functor from usual sets to pointed sets , but it is not full and these categories are not equivalent .. faithful functor. faithful functor. equivalent. Equivalence of categories. In particular , the empty set is not a pointed set , for it has no element that can be chosen as base point .. set. Set ( mathematics ). empty set. empty set. The category of pointed sets and based maps is equivalent to but not isomorphic with the category of sets and partial functions .. functions. function ( mathematics ). category. category theory. equivalent. Equivalence of categories. isomorphic. Isomorphism of categories. One textbook notes that `` This formal completion of sets and partial maps by adding ` improper ' , ` infinite ' elements was reinvented many times , in particular , in topology -LRB- one-point compactification -RRB- and in theoretical computer science . ''. one-point compactification. one-point compactification. theoretical computer science. theoretical computer science. The category of pointed sets and pointed maps is isomorphic to the co-slice category , where is a singleton set .. set. Set ( mathematics ). category. category theory. singleton set. singleton set. isomorphic. Isomorphism of categories. co-slice category. co-slice category. The category of pointed sets and pointed maps has both products and co-products , but it is not a distributive category .. category. category theory. distributive category. distributive category. It is also an example of a category where is not isomorphic to .. category. category theory. isomorphic. Isomorphism of categories. Many algebraic structures are pointed sets in a rather trivial way .. For example , groups are pointed sets by choosing the identity element as the basepoint , so that group homomorphisms are point-preserving maps .. groups. Group ( mathematics ). identity element. identity element. This observation can be restated in category theoretic terms as the existence of a forgetful functor from groups to pointed sets .. category. category theory. groups. Group ( mathematics ). forgetful functor. forgetful functor. A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element .. set. Set ( mathematics ). pointed space. pointed space. discrete topology. discrete topology. vector space. vector space. field with one element. field with one element. As `` rooted set '' the notion naturally appears in the study of antimatroids and transportation polytopes .. set. Set ( mathematics )
not_related.