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On the structure of perfect sets in various topologies associated with tree forcings

Andrzej Nowik, Patrick Reardon (2013)

Open Mathematics

We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.

On ω -resolvable and almost- ω -resolvable spaces

J. Angoa, M. Ibarra, Angel Tamariz-Mascarúa (2008)

Commentationes Mathematicae Universitatis Carolinae

We continue the study of almost- ω -resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost- ω -resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded T 0 space with countable tightness and every T 1 space with π -weight ≤ ℵ 1 is hereditarily almost- ω -resolvable, (2) every crowded paracompact T 2 space which is the closed preimage of a crowded Fréchet T 2 space in such a way that the...

Partial discretization of topologies

M. Bonanzinga, F. Cammaroto, M. V. Matveev (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.

Pointwise density topology

Magdalena Górajska (2015)

Open Mathematics

The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density...

Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)

Commentationes Mathematicae Universitatis Carolinae

Given a Tychonoff space X , a base α for an ideal on X is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on α converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

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