mathematics, the cylinder sets form a basis of the product topology on a product of sets; they are also a generating family of the cylinder σ-algebra. Given...

In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional...

may be breathing gas used with a scuba set, in which case the cylinder may also be referred to as a scuba cylinder, scuba tank or diving tank. When used...

Cylinder (optometry) Cylinder, Iowa, a city in Palo Alto County, Iowa, United States Cylinder set, a natural basic set in product spaces Cylinder set...

_{n}(v))\in E\right\}.} Any set of this type is called a cylinder set. The collection of all cylinder sets forms an algebra of sets in H , {\displaystyle H...

main gas cylinder or cylinders. This arrangement is particularly popular with twin or double cylinder sets, and can be used to carry larger sets of three...

The cylinders are then the generators for the cylinder sets: the cylinder sets then consist of all intersections of a finite number of cylinders. That...

Phonograph cylinders (also referred to as Edison cylinders after its creator Thomas Edison) are the earliest commercial medium for recording and reproducing...

equality. The cylindric algebra should not be confused with the measure theoretic concept cylindrical algebra that arises in the study of cylinder set measures...

on Banach spaces. For a product space, the cylinder σ-algebra is the one that is generated by cylinder sets. In the context of a Banach space X {\displaystyle...

primary gas supply failure. A bailout cylinder may be carried by a scuba diver in addition to the primary scuba set, or by a surface supplied diver using...

is the set of natural numbers and X {\displaystyle X} is a set of real-valued sequences. In this case, it suffices to consider the cylinder sets C n (...

The cylinder is the power-producing element of the steam engine powering a steam locomotive. The cylinder is made pressure-tight with end covers and a...

also be identified with the set of 2-adic integers. The basis for the open sets of the product topology are cylinder sets; the homeomorphism maps these...

of functions considered as sets. Let A {\displaystyle A} be a set and B ⊆ A {\displaystyle B\subseteq A} . Then the cylinder of B {\displaystyle B} with...

A graduated cylinder, also known as a measuring cylinder or mixing cylinder, is a common piece of laboratory equipment used to measure the volume of a...

taken as "don't care". These sets of finite sequences are referred to as cylinder sets in the product topology. The set of all such strings forms a sigma...

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions around a main axis (a chosen directed line) and...

Removing the cylinder typically requires only loosening a set screw, then sliding the cylinder from the boltwork. The second is that it is usually possible...

\{H\},\{T\},S\}.} The set X j − 1 ( B ) {\displaystyle X_{j}^{-1}(B)} for some B ∈ Σ {\displaystyle B\in \Sigma } is then a cylinder set, consisting of all...

An O'Neill cylinder (also called an O'Neill colony, or Island Three) is a space settlement concept proposed by American physicist Gerard K. O'Neill in...

out of a gas storage cylinder a scuba cylinder valve to control the flow of gas into or out of the diving cylinders of a scuba set a valve to control flow...

shaped in the form of a perfect circle, extended vertically into a cylinder, set inside a square that fleshed out the remainder of the building. It seated...

complements of the cylinder sets then form the Borel set A {\displaystyle {\mathcal {A}}} defined above. In formal terms, the cylinder sets form the base for...

A gas cylinder is a pressure vessel for storage and containment of gases at above atmospheric pressure. Gas storage cylinders may also be called bottles...

while still using reasonably small cylinders. By having valves to enable switching between banks, one set of cylinders can be taken off-line while another...

{\displaystyle \tau (s)_{k}=s_{k+1}} This set has a natural product topology; the base for this topology are the cylinder sets C m [ ξ 0 , … , ξ k ] = { s ∈ Q Z...

Telescopic cylinders are a special design of a hydraulic cylinder or pneumatic cylinder as well as pulley system which provide an exceptionally long output...

In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about...

V^{\mathbb {Z} }} ⁠ is a countable union of cylinder sets. Every open set in the subshift is the intersection of an open set of ⁠ V Z {\displaystyle V^{\mathbb...