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The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
[1] [2] A function f : X → Y between topological spaces has a closed graph if its graph is a closed subset of the product space X × Y. A related property is open graph. [3] This property is studied because there are many theorems, known as closed graph theorems, giving conditions under which a function with a closed graph is necessarily ...
This is a list of the instructions that make up the Java bytecode, an abstract machine language that is ultimately executed by the Java virtual machine. [1] The Java bytecode is generated from languages running on the Java Platform, most notably the Java programming language.
A HTTP tunnel can also be implemented using only the usual HTTP methods as POST, GET, PUT and DELETE. This is similar to the approach used in Bidirectional-streams Over Synchronous HTTP ( BOSH ). A special HTTP server runs outside the protected network and a client program is run on a computer inside the protected network.
A singleton implementation may use lazy initialization in which the instance is created when the static method is first invoked. In multithreaded programs, this can cause race conditions that result in the creation of multiple instances. The following Java 5+ example [6] is a thread-safe implementation, using lazy initialization with double ...
The Java Class Library (JCL) is a set of dynamically loadable libraries that Java Virtual Machine (JVM) languages can call at run time. Because the Java Platform is not dependent on a specific operating system , applications cannot rely on any of the platform-native libraries.
The usual proof of the closed graph theorem employs the open mapping theorem.It simply uses a general recipe of obtaining the closed graph theorem from the open mapping theorem; see closed graph theorem § Relation to the open mapping theorem (this deduction is formal and does not use linearity; the linearity is needed to appeal to the open mapping theorem which relies on the linearity.)
For example, in the book Topology and Groupoids, where the condition given for the statement below is that and . The pasting lemma is crucial to the construction of the fundamental group and fundamental groupoid of a topological space ; it allows one to concatenate paths to create a new path.