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Neighborhood base at the identity of free paratopological groups

Ali Sayed Elfard (2013)

Topological Algebra and its Applications

In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.

Non-subharmonicity of the Hausdorff distance

Edoardo Vesentini (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.

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