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Natural sinks on Y β

J. Schröder (1992)

Commentationes Mathematicae Universitatis Carolinae

Let ( e β : 𝐐 Y β ) β Ord be the large source of epimorphisms in the category Ury of Urysohn spaces constructed in [2]. A sink ( g β : Y β X ) β Ord is called natural, if g β e β = g β ' e β ' for all β , β ' Ord . In this paper natural sinks are characterized. As a result it is shown that Ury permits no ( E p i , ) -factorization structure for arbitrary (large) sources.

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.

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