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A Note on Regular-closed Functions

Takashi Noiri (1981)

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

Se X ed Y sono spazi topologici, una funzione f : X Y è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di X in un insieme chiuso di Y . Si dimostra che una funzione regolarmente chiusa f : X Y risulta chiusa se X è normale.

A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura (2002)

Fundamenta Mathematicae

Let n be an integer with n ≥ 2 and X i be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of Σ ( i X i ) with those of i Σ X i (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.

A note on -spaces and g -metrizable spaces

Zhaowen Li (2005)

Czechoslovak Mathematical Journal

In this paper, we give the mapping theorems on -spaces and g -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π -mappings.

A note on spaces with countable extent

Yan-Kui Song (2017)

Commentationes Mathematicae Universitatis Carolinae

Let P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X , there exists a subspace A X with property P such that X = S t ( A , 𝒰 ) . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

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