Compactifications and uniformities on sigma frames

Joanne L. Walters-Wayland

Displaying similar documents to “Compactifications and uniformities on sigma frames”

On the cardinality and weight spectra of compact spaces, II

Istvan Juhász, Saharon Shelah (1998)

Fundamenta Mathematicae

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Let B(κ,λ) be the subalgebra of P(κ) generated by ${[κ]}^{\leq λ}$ . It is shown that if B is any homomorphic image of B(κ,λ) then either $| B | < 2^{λ}$ or $| B | = {| B |}^{λ}$ ; moreover, if X is the Stone space of B then either $| X | \leq 2^{2^{λ}}$ or $| X | = | B | = {| B |}^{λ}$ . This implies the existence of 0-dimensional compact $T_{2}$ spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.

Intersection topologies with respect to separable GO-spaces and the countable ordinals

M. Jones (1995)

Fundamenta Mathematicae

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Given two topologies, $T_{1}$ and $T_{2}$ , on the same set X, the intersection topologywith respect to $T_{1}$ and $T_{2}$ is the topology with basis $U_{1} \cap U_{2} : U_{1} \in T_{1}, U_{2} \in T_{2}$ . Equivalently, T is the join of $T_{1}$ and $T_{2}$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and $ω_{1}$ -compactness in this class of topologies. We demonstrate that the majority of his results...

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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Let $F_{i} = 1, . . ., N$ be affine mappings of $ℝ^{n}$ . It is well known that if there exists j ≤ 1 such that for every $σ_{1}, . . ., σ_{j} \in 1, . . ., N$ the composition (1) $F_{σ 1} \circ . . . \circ F_{σ_{j}}$ is a contraction, then for any infinite sequence $σ_{1}, σ_{2}, . . . \in 1, . . ., N$ and any $z \in ℝ^{n}$ , the sequence (2) $F_{σ 1} \circ . . . \circ F_{σ_{n}} (z)$ is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any $z \in ℝ^{n}$ and any $σ = σ_{1}, σ_{2}, . . .$ belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every $σ = σ_{1}, σ_{2}, . . . \in Σ$ the composition (1) is a contraction....

A note on evaluations of some exponential sums

Marko J. Moisio (2000)

Acta Arithmetica

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1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form $S (a, p^{α} + 1) : = \sum_{x \in_{q}} χ (a x^{p^{α} + 1})$ where χ is a non-trivial additive character of the finite field $_{q}$ , $q = p^{e}$ odd, and $a \in *_{q}$ . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of $p^{α} + 1$ . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate...

On the positivity of the number of t-core partitions

Ken Ono (1994)

Acta Arithmetica

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A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n .$ Here we define a special class of partitions. 1. Let $t \geq 1$ be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof $n .$ The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3,4,6]. If $t \geq 1$ and $n \geq 0$ ,...

On the preservation of separation axioms in products

Milan Z. Grulović, Miloš S. Kurilić (1992)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient and necessary conditions to be fulfilled by a filter $Ψ$ and an ideal $Λ$ in order that the $Ψ$ -quotient space of the $Λ$ -ideal product space preserves $T_{k}$ -properties ( $k = 0, 1, 2, 3, 3 \frac{1}{2}$ ) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.

Generalized linearly ordered spaces and weak pseudocompactness

Oleg Okunev, Angel Tamariz-Mascarúa (1997)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove that if $X$ is a generalized linearly ordered space, and either (i) each proper open interval in $X$ is truly weakly pseudocompact, or (ii) $X$ is paracompact and each point of $X$ has a truly weakly pseudocompact neighborhood, then $X$ is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].