{\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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

final round is played on the third Sunday. The U.S. Open is staged at a variety of courses, set up in such a way that scoring is very difficult, with...

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

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...

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...

Daniil Medvedev in a five-set final to win his first major title. He followed by winning three Masters 1000 events, the US Open, and the ATP Finals to finish...

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...

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...

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...

below represent career winning percentages of players that are retired (regular font) as well as current active players (boldface). The latter are subject...

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...

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