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Some weak covering properties and infinite games

Masami Sakai — 2014

Open Mathematics

We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz...

Selection principles and upper semicontinuous functions

Masami Sakai — 2009

Colloquium Mathematicae

In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and $S_{f i n} (Γ, Ω)$ in terms of upper semicontinuous functions

On supertightness and function spaces

Masami Sakai — 1988

Commentationes Mathematicae Universitatis Carolinae

Notes on strongly Whyburn spaces

Masami Sakai — 2016

Commentationes Mathematicae Universitatis Carolinae

We introduce the notion of a strongly Whyburn space, and show that a space $X$ is strongly Whyburn if and only if $X \times (ω + 1)$ is Whyburn. We also show that if $X \times Y$ is Whyburn for any Whyburn space $Y$ , then $X$ is discrete.

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf

Masami Sakai — 1992

Commentationes Mathematicae Universitatis Carolinae

A.V. Arkhangel’skii asked that, is it true that every space $Y$ of countable tightness is homeomorphic to a subspace (to a closed subspace) of $C_{p} (X)$ where $X$ is Lindelöf? $C_{p} (X)$ denotes the space of all continuous real-valued functions on a space $X$ with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace of $C_{p} (X)$ ...

Mapping theorems on $ℵ$ -spaces

Masami Sakai — 2008

Commentationes Mathematicae Universitatis Carolinae

In this paper we improve some mapping theorems on $ℵ$ -spaces. For instance we show that an $ℵ$ -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an $ℵ$ -space is preserved by a closed and open map.

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Currently displaying 1 – 6 of 6

Some weak covering properties and infinite games

Selection principles and upper semicontinuous functions

On supertightness and function spaces

Notes on strongly Whyburn spaces

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf

Mapping theorems on $ℵ$ -spaces

Advanced Search

Formula preview

Currently displaying 1 – 6 of 6

Some weak covering properties and infinite games

Selection principles and upper semicontinuous functions

On supertightness and function spaces

Notes on strongly Whyburn spaces

On embeddings into C p ( X ) where X is Lindelöf

Mapping theorems on ℵ -spaces

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf

Mapping theorems on $ℵ$ -spaces