Some Decision Problems of Enormous Complexity - OSU
... function is finite if and only if its domain is finite if and only if its 1-domain is finite. We write dom(f) for the domain of f and 1-dom(f) for the 1-domain of f. Let f be a k-ary function and E ⊆ 1-dom(f). We write k f|E for the restriction of f to E . Thus f|E ⊆ f, dom(f|E) = k E , and 1-dom(f| ...
... function is finite if and only if its domain is finite if and only if its 1-domain is finite. We write dom(f) for the domain of f and 1-dom(f) for the 1-domain of f. Let f be a k-ary function and E ⊆ 1-dom(f). We write k f|E for the restriction of f to E . Thus f|E ⊆ f, dom(f|E) = k E , and 1-dom(f| ...
COMPLETION FUNCTORS FOR CAUCHY SPACES
... denotes the filter generated on X by- (considered as a filter base on X). If (X, C) is a complete Cauchy space (i.e. convergence space), then it will be necessary to distinguish between a convergence subspace (a subspace in the usual convergence space sense) and a Cauchy subspace (with the meaning d ...
... denotes the filter generated on X by- (considered as a filter base on X). If (X, C) is a complete Cauchy space (i.e. convergence space), then it will be necessary to distinguish between a convergence subspace (a subspace in the usual convergence space sense) and a Cauchy subspace (with the meaning d ...
A Concise Course in Algebraic Topology JP May
... exposition of this approach in the literature, at any level. More centrally, there now exist axiomatic treatments of large swaths of homotopy theory based on Quillen’s theory of closed model categories. While I do not think that a first course should introduce such abstractions, I do think that the ...
... exposition of this approach in the literature, at any level. More centrally, there now exist axiomatic treatments of large swaths of homotopy theory based on Quillen’s theory of closed model categories. While I do not think that a first course should introduce such abstractions, I do think that the ...
Projective ideals in rings of continuous functions
... l Preliminaries* Let X be a completely regular, Hausdorff space and C(X) be the ring of real-valued continuous functions on X. An ideal in C(X) is said to be projective provided it is a projective C(X)-module. In [1], Bkouche has shown that if X is locally compact then CK(X), the ideal of functions ...
... l Preliminaries* Let X be a completely regular, Hausdorff space and C(X) be the ring of real-valued continuous functions on X. An ideal in C(X) is said to be projective provided it is a projective C(X)-module. In [1], Bkouche has shown that if X is locally compact then CK(X), the ideal of functions ...
