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An internal characterisation of radiality
... nests’; one coming from the ω + 1 factor and the other coming from the ω1 + 1 factor. However, it is not radial because for any such transfinite sequence, its projections must also converge. This is not possible to due conflicting cofinalities in the different factors. So what makes one space radial ...
... nests’; one coming from the ω + 1 factor and the other coming from the ω1 + 1 factor. However, it is not radial because for any such transfinite sequence, its projections must also converge. This is not possible to due conflicting cofinalities in the different factors. So what makes one space radial ...
γ-SETS AND γ-CONTINUOUS FUNCTIONS
... semi-open subsets in X is a γ-set. Proof. Let U1 and U2 be semi-open sets in X. For each x ∈ U1 ∩U2 , we get U1 ∩U2 ∈ Sx . Thus, from the concept of the semi-convergence of filters, whenever every filter F semi-converges to x, U1 ∩ U2 ∈ F . Definition 2.6. Let (X, τ) be a topological space. The γ-in ...
... semi-open subsets in X is a γ-set. Proof. Let U1 and U2 be semi-open sets in X. For each x ∈ U1 ∩U2 , we get U1 ∩U2 ∈ Sx . Thus, from the concept of the semi-convergence of filters, whenever every filter F semi-converges to x, U1 ∩ U2 ∈ F . Definition 2.6. Let (X, τ) be a topological space. The γ-in ...
Lecture 8
... non-compact spaces, it is natural to ask the following question: can a given space be embedded homeomorphically in a compact space? The answer to this is always yes. In fact, there are many ways of doing it, among them the Wallman, Stone-Čech and Alexandroff compactifications. Today we consider onl ...
... non-compact spaces, it is natural to ask the following question: can a given space be embedded homeomorphically in a compact space? The answer to this is always yes. In fact, there are many ways of doing it, among them the Wallman, Stone-Čech and Alexandroff compactifications. Today we consider onl ...
How to find a Khalimsky-continuous approximation of a real-valued function Erik Melin
... Unless otherwise stated we shall assume that Z is equipped with the Khalimsky topology from now on. This makes it meaningful to consider (for example) continuous functions f : Z → Z. Continuous integer-valued functions will sometimes be called Khalimsky-continuous, if we want to stress that a functi ...
... Unless otherwise stated we shall assume that Z is equipped with the Khalimsky topology from now on. This makes it meaningful to consider (for example) continuous functions f : Z → Z. Continuous integer-valued functions will sometimes be called Khalimsky-continuous, if we want to stress that a functi ...
Unwinding and integration on quotients
... [3.0.2] Theorem: Let V ⊂ Cco (G) be a quasi-complete locally convex [5] topological vector space of complexvalued functions on G stable under left and right translations, and containing an approximate identity {ϕi }. In this context, an approximate identity on R a topological group G is a sequence o ...
... [3.0.2] Theorem: Let V ⊂ Cco (G) be a quasi-complete locally convex [5] topological vector space of complexvalued functions on G stable under left and right translations, and containing an approximate identity {ϕi }. In this context, an approximate identity on R a topological group G is a sequence o ...