The Pytkeev property and the Reznichenko property in function spaces

Authors

  • Masami Sakai

DOI:

https://doi.org/10.1285/i15900932v22n2p43

Keywords:

Function space, Topology of pointwise convergence, Sequential, Countable tightness, Pytkeev space, Weakly Fréchet-Urysohn, $omega$ -cover, $omega$-shrinkable, $omega$-grouping property, The Menger property, The Rothberger property, The Hurewicz property, Universal measure zero, Perfectly meager, Property $(gamma)$

Abstract

For a Tychonoff space $X$ we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. Characterizations of sequentiality and countable tightness of $C_p(X)$ in terms of $X$ were given by Gerlits, Nagy, Pytkeev and Arhangel'skii.  In this paper, we characterize the Pytkeev property and the Reznichenko property of $C_p(X)$ in terms of $X$.  In particular we note that if $C_p(X)$ over a subset $X$ of the real line is a Pytkeev space, then $X$ is perfectly meager and has universal measure zero.

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Published

29-10-2003

Issue

Volume 22, Issue 2 (2003)

Section

Articoli

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