{\displaystyle S} of a topological space X {\displaystyle X} is called a regular open set if it is equal to the interior of its closure; expressed symbolically...

In mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set with a distance defined between every two...

topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods. Thus p and...

more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function f : X → Y {\displaystyle...

open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of...

topological space whose regular open sets (sets that equal the interiors of their closures) form a base for the topology. Every regular space is semiregular...

Interface (POSIX) Base Specifications, Issue 7 Regular Expressions, IEEE Std 1003.1-2024, Open Group Open source list of regular expression resources...

successive open strings Regular character, a main character who appears more frequently and/or prominently than a recurring character Regular division of...

mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable sets and from...

the regular open sets form a base for the open sets of X. Any regular space must also be semiregular. X is quasi-regular if for any nonempty open set G...

Quintel attended many open shows at CalArts, an eight-hour festival of student animation. The style and sensibility of Regular Show was difficult to work...

Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These...

set Open set Clopen set Fσ set Gδ set Compact set Relatively compact set Regular open set, regular closed set Connected set Perfect set Meagre set Nowhere...

June 1996, expansion sets were released in a regular pattern: the base sets were released in October with the small expansion sets being released in February...

is complete. The algebra of subsets of a given set is a complete Boolean algebra. The regular open sets of any topological space form a complete Boolean...

space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A...

associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U...

T {\displaystyle T} , we can also consider the collection of its regular open sets. This is a frame using as join the interior of the closure of the...

to "A Regular Epic Final Battle", Mordecai quits The Park, parts ways with Rigby, moves to New York City, and returns to making art. He opens a successful...

a convex set C {\displaystyle C} is non-empty then C {\displaystyle C} is a closed (respectively, open) set if and only if it is a regular closed (respectively...

mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its...

The Canons Regular of St. Augustine are Catholic priests who live in community under a rule (Latin: regula and κανών, kanon, in Greek) and are generally...

regular tunings have equal musical intervals between the paired notes of their successive open strings. Guitar tunings assign pitches to the open strings...

collapsing algebras. If κ and λ are cardinals, then the Boolean algebra of regular open sets of the product space κλ is a collapsing algebra. Here κ and λ are...

behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic". The Julia set of a function  f  is commonly denoted...

constructed as the algebra of regular open sets in the topological space of P (with underlying set P, and a base given by the sets Up of elements q with q≤p)...

In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa }...

opposite of the nth digit of the nth definable real number RO The regular open sets of a topological space or poset Rowbottom 1.  Frederick Rowbottom...

of a rebreather dive is longer than an open-circuit dive, for similar weight and bulk of the set, if the set is bigger than the practical lower limit...

Beyond Euclidean space, there is an infinite set of regular hyperbolic tilings. The five convex regular polyhedra are called the Platonic solids. The...