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  2. Subset - Wikipedia

    en.wikipedia.org/wiki/Subset

    A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.

  3. Space (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Space_(mathematics)

    In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same structure.

  4. Sober space - Wikipedia

    en.wikipedia.org/wiki/Sober_space

    The prime spectrum Spec(R) of a commutative ring R with the Zariski topology is a compact sober space. [3] In fact, every spectral space (i.e. a compact sober space for which the collection of compact open subsets is closed under finite intersections and forms a base for the topology) is homeomorphic to Spec(R) for some commutative ring R.

  5. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    2. A proper subset of a set X is a subset not equal to X. 3. A proper forcing is a forcing notion that does not collapse any stationary set 4. The proper forcing axiom asserts that if P is proper and D α is a dense subset of P for each α<ω 1, then there is a filter G P such that D α ∩ G is nonempty for all α<ω 1

  6. Glossary of general topology - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_general_topology

    The regular open subsets of a space form a complete Boolean algebra. [21] Relatively compact A subset Y of a space X is relatively compact in X if the closure of Y in X is compact. Residual If X is a space and A is a subset of X, then A is residual in X if the complement of A is meagre in X. Also called comeagre or comeager. Resolvable

  7. Interior (topology) - Wikipedia

    en.wikipedia.org/wiki/Interior_(topology)

    In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

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