topological space
- noun
- /ˌtɒpəˈlɒdʒɪkəl speɪs/
- Specialized
:
espacio topológico
- The nature of topological space is to be a space of relations from end to end: not extensive but intensive, as Deleuze would say.
So let capital X be a topological space.
- So let capital X be a topological space.
Examples
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A topology is usually defined on a given set X as a subset of the power set of X. Then, given this topology, the neighborhoods of each point of the topological space are defined.
Academic text (1998) -
This is open in X because X is a topological space, so Y is open in Y.
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The pair (X, T) is called a topological space.
Academic text (1998) -
So this is how we define convergence for topological space three.
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So here he gets into topological spaces and gives the general definition of a topology.
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In this sense, topological space differs from Euclidean space in that it doesn't have empty areas.
Academic text (2017) -
For living beings, transductive operations can no longer apply to propagating a piece of information through a homogeneous Euclidean space, but are more like operations within a topological space.
Academic text (2017) -
Definition 2. Let (X, T) be a topological space, and for each x in X, let U_o(x) := W, where W is an element of T: x is an element of W; then the elements of U_o(x) are called the open neighborhoods of x with respect to T. The family of sets
Academic text (1998) -
In mathematics, a topological space is essential for understanding the behavior of functions and continuity.
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For a set to be considered a topological space, it must satisfy specific axioms regarding its open sets.
Surface Forms
Morphology
topological + space
The phrase is a straightforward adjective+noun composition meaning ‘a space characterized by topological properties’, so its general sense (a type of space defined by topology) is predictable from the constituents. However, the precise technical content (the collection of open sets and specific axioms) is domain-specific and not fully inferable from the words alone, so learners would only get a partial understanding.
Etymology
Topological space comes from topological (about shapes and how things are connected) and space (a place or collection of points), like a rubber sheet with points and areas you can stretch without tearing. So, it means a 'set of points' with simple rules about which parts are 'open' or connected.
