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2. Form (architecture) - Wikipedia

   en.wikipedia.org/wiki/Form_(architecture)

   The focus shifted towards the forms of medieval vernacular architecture with architect and builder being the same person. Following idealism of Fichte, Schelling and Hegel, [40] the designers of Arts and Crafts movement saw their job as personal artistic expression unbounded by old traditions (cf. "Free style" of Charles Rennie Mackintosh). New ...

3. Order complete - Wikipedia

   en.wikipedia.org/wiki/Order_complete

   In mathematics, specifically in order theory and functional analysis, a subset of an ordered vector space is said to be order complete in if for every non-empty subset of that is order bounded in (meaning contained in an interval, which is a set of the form [,]:= {:}, for some ,), the supremum ' and the infimum both exist and are elements of .

4. Space form - Wikipedia

   en.wikipedia.org/wiki/Space_form

   In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three most fundamental examples are Euclidean n -space , the n -dimensional sphere , and hyperbolic space , although a space form need not be simply connected .

5. The Nature of Order - Wikipedia

   en.wikipedia.org/wiki/The_Nature_of_Order

   The Nature of Order: An Essay on the Art of Building and the Nature of the Universe (ISBN 0-9726529-0-6) is a four-volume work by the architect Christopher Alexander published in 2002–2004. In his earlier work, Alexander attempted to formulate the principles that lead to a good built environment as patterns , or recurring design solutions.

6. Order topology (functional analysis) - Wikipedia

   en.wikipedia.org/wiki/Order_topology_(functional...

   In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space (,) is the finest locally convex topological vector space (TVS) topology on for which every order interval is bounded, where an order interval in is a set of the form [,]:= {:} where and belong to . [1]

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8. Order topology - Wikipedia

   en.wikipedia.org/wiki/Order_topology

   Though the subspace topology of Y = {−1} ∪ {1/n } n∈N in the section above is shown not to be generated by the induced order on Y, it is nonetheless an order topology on Y; indeed, in the subspace topology every point is isolated (i.e., singleton {y} is open in Y for every y in Y), so the subspace topology is the discrete topology on Y (the topology in which every subset of Y is open ...

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