# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

In this definition, a polytope is the union of finitely many simplices, with the additional property that, for any two simplices that have a nonempty intersection, their intersection is a vertex, edge, or higher dimensional face of the two.

A Baire space is a topological space with the following property: for each countable collection of open dense sets U < sub > n </ sub >, their intersection ∩ U < sub > n </ sub > is dense.

The proof is similar to the preceding statement ; the finite intersection property takes the role played by completeness.

But ( 0, 1 ) clearly cannot be written as a union of the elements of S. Using the alternate definition, the second property fails, since no base element can " fit " inside this intersection.

Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors.

When the Claretians sold their Claretville property in 1978 to Clare Prophet and her Church Universal and Triumphant ( CUT ) cult, Thomas Aquinas College purchased, moved to, and began construction on a permanent campus in Santa Paula, CA At the present time, the Gillette Estate / Claretville property is now known as the ' King Gillette Ranch ' and this property remains at the intersection of Mulholland Highway and Las Virgenes Road in Calabasas.

The property was originally a large farm known as Mayfair, whose 1812 stone house remains overlooking Greenpoint Road near its intersection with Avebury Road.

Ladue was named from Ladue Road, the main thoroughfare in the area that led from St. Louis City to wealthy entrepeneur Peter Albert LaDue's large property at the current intersection of Warson Rd.

During World War II, the Army Air Corps established a landing field for flight training on property near the present-day intersection of Main and Wheatland roads.

Likewise, it is analogous to the finite intersection property characterization of compactness in topological spaces: a collection of closed sets in a compact space has a non-empty intersection if every finite subcollection has a non-empty intersection.

The area was a lemon grove until 1903, when Daeida Beveridge allowed one corner of the dirt intersection on her property to be used for the building of the Hollywood Memorial Church for the local German Methodist population.

In general topology, a branch of mathematics, a collection A of subsets of a set X is said to have the finite intersection property if the intersection over any finite subcollection of A is nonempty.

A centered system of sets is a collection of sets with the finite intersection property.

Then the collection has the finite intersection property ( fip ), if any finite subcollection has non-empty intersection

The finite intersection property is useful in formulating an alternative definition of compactness: a space is compact if and only if every collection of closed sets satisfying the finite intersection property has nonempty intersection itself.

* The intersection of any collection of equivalence relations over X ( viewed as a subset of X × X ) is also an equivalence relation.

Leipzig is also situated at the intersection of the ancient roads known as the Via Regia ( King's highway ), which traversed Germanic lands in an east-west direction, and Via Imperii ( Imperial Highway ), a north-south road.

This also works for the greatest common divisor ( GCD ), except that instead of multiplying all of the numbers in the Venn diagram, one multiplies only the prime factors that are in the intersection.

Although an eclipse can only occur when the Moon is either new or full, it must also be positioned very near the intersection of Earth's orbit plane about the Sun and the Moon's orbit plane about the Earth ( that is, at one of its nodes ).

At times, Sakamoto would also present varying interpretations of technology's intersection with music: He would present some pieces, such as " Replica ", with Kraftwerkian rigidity and order, while he would infuse humanity and humor into others – " Broadway Boogie Woogie ", for example, liberally lifts samples from Ridley Scott's film Blade Runner and pairs them with a raucous, sax-driven techno-pop backdrop.

For instance, the intersection lineation of a S < sub > 1 </ sub > cleavage and bedding is the L < sub > 1-0 </ sub > intersection lineation ( also known as the cleavage-bedding lineation ).

Bucharest is also a major intersection of Romania's national road network.

Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.

weak intersection it is only possible to move a stone horizontally and vertically, while on a strong intersection it is also possible to move a stone diagonally.

A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center.

As another example, we can also consider the set of all finite or cofinite subsets of X, again with symmetric difference and intersection as operations.

Note that these properties are also satisfied if " interior ", " subset ", " union ", " contained in ", " largest " and " open " are replaced by " closure ", " superset ", " intersection ", " which contains ", " smallest ", and " closed ", respectively.

In the mathematical subfield of linear algebra or more generally functional analysis, the linear span ( also called the linear hull ) of a set of vectors in a vector space is the intersection of all subspaces containing that set.

This graph also shows that as long as P < sub > tariff </ sub > does not fall above the intersection of the Supply and Demand lines, then an equilibrium can be reached in which there are no shortages of demand or excesses of supply, and so Japan's industry can produce and sell widgets to the same degree as manufacturers in any other country.

Examples also exist in Bracknell, Hull, Nottingham and Reading, as well as on the N2 / M50 intersection in Dublin, Ireland.

It is also the name of the region of the theater district ( and, at times, the red-light district ) near that intersection.

In 1900 the community of Lickskillet, also known as Esco was located about north of Manardville near what today is the intersection of Old State Route 33 and Fall Creek or Cox Road with TN 170.

Perrysville is also located along the Wabash River, on State Road 32 just east of its intersection with State Road 63.

Van Buren Township, which contains Veedersburg, also includes Stone Bluff ; and Shawnee Township to the north of Van Buren holds the hamlets of Fountain ( on the banks of the Wabash ) and Rob Roy ( at the intersection of U. S. Route 41 and State Road 55 ).

The headquarters of Banca Transilvania, at the intersection of Regele Ferdinand Avenue and Bariţiu Street, is also a large contemporary building and was originally constructed to host the regional offices of Romtelecom, the public phone company, but was later sold to the bank.

The ring of integers of a number field K, denoted by O < sub > K </ sub >, is the intersection of K and A: it can also be characterised as the maximal order of the field K.

This allows left-turn traffic, which often consists of just a few cars, to vacate the intersection quickly before giving priority to vehicles traveling straight.

This allows a reduction in the length of the pedestrian phase at signalized intersection, and reduces the time needed to yield to pedestrians at stop sign controlled intersections.

This shortcut allows that traffic to skip an often busy intersection and head out of the village on North Chestnut Street.

A pedestrian scramble, also known as an < nowiki >' X ' Crossing </ nowiki > ( UK ), diagonal crossing ( US ), scramble intersection ( Canada ), and, more poetically, a Barnes Dance, is a pedestrian crossing system that stops all vehicular traffic and allows pedestrians to cross an intersection in every direction, including diagonally, at the same time.

The intersection of 97 Street, having seven through lanes, with Yellowhead Trail in Edmonton, Alberta, Canada, though a diamond interchange in concept, required such a wide bridge that traffic-signal phasing allows this intersection to behave as a SPUI.

It also allows easier creation of a green wave by adjusting traffic lights on the through route, because fewer phases are needed at each intersection.

The lake has not been studied extensively, but it is believed that the lake is at the intersection of two faults, which allows oil from a deep deposit to be forced up.

Like the continuous flow intersection, the diverging diamond interchange allows for two-phase operation at all signalized intersections within the interchange.

This will allow motorists to clearly see the driving lanes at all times through the intersection, and allows vehicles approaching the highway to determine the edge of KY 9.