On the t-equivalence relation

Krupski, Mikołaj

doi:10.1016/j.topol.2012.11.015

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…In Section 4 we prove our main result (Theorem 4.1). The technique which we use in the proof differs form the technique used in [Kr2] and is inspired by some ideas from [Ok] and [Kr1]. Next we derive some corollaries to Theorem 4.1.…”

Section: Introductionmentioning

confidence: 99%

On the weak and pointwise topologies in function spaces II

Krupski¹,

Marciszewski²

2017

Journal of Mathematical Analysis and Applications

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Abstract. For a compact space K we denote by C w (K) (C p (K)) the space of continuous real-valued functions on K endowed with the weak (pointwise) topology. In this paper we discuss the following basic question which seems to be open: Let K and L be infinite compact spaces. Can it happen that C w (K) and C p (L) are homeomorphic?M. Krupski proved that the above problem has a negative answer when K = L and K is finite-dimensional and metrizable. We extend this result to the class of finite-dimensional Valdivia compact spaces K.

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Section: Introductionmentioning

confidence: 99%

On the weak and pointwise topologies in function spaces II

Krupski¹,

Marciszewski²

2017

Journal of Mathematical Analysis and Applications

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“…[4,7]); however, to deal with the weak topology on C(K ) we consider measures on the compact space K rather than points of that space, as it was done in [4,5,7]. One of the key ingredients of the proof is Lemma 1 below.…”

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confidence: 99%

On the weak and pointwise topologies in function spaces

Krupski

2015

RACSAM

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For a compact space K we denote by C w (K ) (C p (K )) the space of continuous real-valued functions on K endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose that K is an infinite (metrizable) compact space. Can C w (K ) and C p (K ) be homeomorphic? We show that the answer is "no", provided K is an infinite compact metrizable C-space. In particular our proof works for any infinite compact metrizable finite-dimensional space K .

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Linear homeomorphisms of function spaces and the position of a space in its compactification

Krupski

2023

Can. J. Math.-J. Can. Math.

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An old question of Arhangel’skii asks if the Menger property of a Tychonoff space X is preserved by homeomorphisms of the space $C_p(X)$ of continuous real-valued functions on X endowed with the pointwise topology. We provide affirmative answer in the case of linear homeomorphisms. To this end, we develop a method of studying invariants of linear homeomorphisms of function spaces $C_p(X)$ by looking at the way X is positioned in its (Čech–Stone) compactification.

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On the t-equivalence relation

Cited by 3 publications

References 10 publications

On the weak and pointwise topologies in function spaces II

On the weak and pointwise topologies in function spaces II

On the weak and pointwise topologies in function spaces

Linear homeomorphisms of function spaces and the position of a space in its compactification

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