Baire Spaces and the Wijsman Topology
... In a metrizable space, this is equivalent to having a countablein-itself π-base. Corollary (Zsilinszky, 20??): A space X is separable, metrizable and Baire if and only if (F(X),Twd) is a metrizable and Baire space for each compatible metric d on X. ...
... In a metrizable space, this is equivalent to having a countablein-itself π-base. Corollary (Zsilinszky, 20??): A space X is separable, metrizable and Baire if and only if (F(X),Twd) is a metrizable and Baire space for each compatible metric d on X. ...
¾ - Hopf Topology Archive
... cannot rule out the possibility of a topological model for F(R) as easily: the classical example of A = S the sphere spectrum in the stable homotopy category shows that the morphism 2 1C can be nonzero in this more general context. Nevertheless, F(R) is not topological either, which follows from T ...
... cannot rule out the possibility of a topological model for F(R) as easily: the classical example of A = S the sphere spectrum in the stable homotopy category shows that the morphism 2 1C can be nonzero in this more general context. Nevertheless, F(R) is not topological either, which follows from T ...
Elements of Functional Analysis - University of South Carolina
... other spaces. We omit the subscript when the space in question is understood. In addition, if we define ρ(x, y) := ||x − y|| then it is easy to see that (X, ρ) is a metric space whose metric is induced by the norm. If (xn ) is a sequence in X, we say that xn converges to x0 ∈ X, written xn → x0 , if ...
... other spaces. We omit the subscript when the space in question is understood. In addition, if we define ρ(x, y) := ||x − y|| then it is easy to see that (X, ρ) is a metric space whose metric is induced by the norm. If (xn ) is a sequence in X, we say that xn converges to x0 ∈ X, written xn → x0 , if ...
on generalized closed sets
... X is closed in s(X). The well-known digital line, also called the Khalimsky line, is a T3/4 -space which fails to be T1 . Theorem 3.4. For any space X, (1) [8] T3/4 = Tgs + semi-T1 . (2) [20] T1/2 = Tgs + semi-T1/2 . The results above clarify some connections between the Tgs property and other lower ...
... X is closed in s(X). The well-known digital line, also called the Khalimsky line, is a T3/4 -space which fails to be T1 . Theorem 3.4. For any space X, (1) [8] T3/4 = Tgs + semi-T1 . (2) [20] T1/2 = Tgs + semi-T1/2 . The results above clarify some connections between the Tgs property and other lower ...
Introduction to symmetric spectra I
... category of spectra. All other categories of spectra defined in a similar manner share this disadvantage. This has caused algebraic topologists a lot of frustration: for example, the absence of a monoidal structure means that one does not have a good notion of a ring spectrum. (This problem was solv ...
... category of spectra. All other categories of spectra defined in a similar manner share this disadvantage. This has caused algebraic topologists a lot of frustration: for example, the absence of a monoidal structure means that one does not have a good notion of a ring spectrum. (This problem was solv ...
INTRODUCTION TO TOPOLOGY Contents 1. Basic concepts 1 2
... each other get mapped to points that are ’close’ to each other as well in some sense. The definition generalizes to metric spaces with no change, however, to obtain a notion of continuity for topological spaces, we need a reformulation in terms of open sets only. To this end, we reconsider how conti ...
... each other get mapped to points that are ’close’ to each other as well in some sense. The definition generalizes to metric spaces with no change, however, to obtain a notion of continuity for topological spaces, we need a reformulation in terms of open sets only. To this end, we reconsider how conti ...