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A form is a product of the designer's creativity. An architect's intuition suggests a new form that eventually blossoms, this explains similarities between the buildings with disparate functions built by the same architect; A form is dictated by the prevailing set of attitudes shared by the society, the Zeitgeist ("Spirit of Age"). While ...
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 .
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.
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 .
A subset of a vector space is called a cone if for all real >,.A cone is called pointed if it contains the origin. A cone is convex if and only if +. The intersection of any non-empty family of cones (resp. convex cones) is again a cone (resp. convex cone); the same is true of the union of an increasing (under set inclusion) family of cones (resp. convex cones).
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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Spatiality is a term used in architecture for characteristics that, looked at from a certain aspect, define the quality of a space. [1] In comparison to the term spaciousness, which includes formal, dimensional determination of size—depth, width or height—spatiality is a higher category term.
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