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The relative importance of space and mass can change very quickly: in 1872, Viollet-le-Duc wrote his book, Entretiens sur l'architecture, completely avoiding the use of the word "space" in its modern meaning; just 20 years later August Schmarsow was declaring the primacy of German: Raumgestaltung, "forming the space". [9]
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.
Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location. [17] They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word). [18] A Form is an objective "blueprint" of perfection. [19]
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems : The primary arithmetic (described in Chapter 4 of LoF ), whose models include Boolean arithmetic ;
Bohm, his co-worker Basil Hiley, and other physicists of Birkbeck College worked toward a model of quantum physics in which the implicate order is represented in the form of an appropriate algebra or other pregeometry. They considered spacetime itself as part of an explicate order that is connected to an implicate order that they called pre-space.
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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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 .