Quotient Spaces and Multiplicity of a Base

Филиппов, В. В.

doi:10.1070/sm1969v009n04abeh001291

Cited by 13 publications

(8 citation statements)

References 2 publications

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“…Thus X is metrisable [6 Now we turn to another metrisation theorem for compact spaces. might not form a base for a topology on X.…”

Section: Definitionmentioning

confidence: 99%

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Two theorems on generalised metric spaces

Svetlichny¹

1997

Bull. Austral. Math. Soc.

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We prove that any compact space, and even any countably compact space having the weak topology with respect to a sequence of symmetrisable subspaces, is metrisable. This generalises results of Arhangel'skii and Nedev on metrisability of symmetrisable compact spaces. Also we define and study contraction functions on generalised metric spaces whose topology can be described in terms of a 'distance function' which is not quite a metric. In particular we present necessary and sufficient conditions for a space of countable pseudo-character to be submetrisable in terms of real-valued contraction functions on this space.

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“…Thus X is metrisable [6 Now we turn to another metrisation theorem for compact spaces. might not form a base for a topology on X.…”

Section: Definitionmentioning

confidence: 99%

“…[6,8] Every compact space Laving the weak topology with respect to a sequence of metrisable subspaces is metrisable.…”

Section: Definitionmentioning

confidence: 99%

Two theorems on generalised metric spaces

Svetlichny¹

1997

Bull. Austral. Math. Soc.

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“…Nagata [18] generalized Theorem 4.1 (as well as a result of V. V. Filippov [8,Theorem 3]) by weakening "has a G δ diagonal" to "satisfies (1.2)". We now generalize Nagata's theorem, as well as Theorem 3.1 above, as follows.…”

Section: (Borges-okuyama) a Space X Is Metrizable If And Only If It mentioning

confidence: 99%

“…7 A map /: X-> Y is compact-covering if every compact K C Y is the image of some compact ccx. 8 A modification of Rudin's proof (which also works for countably compact spaces) is given in [7,Proposition 2.1].…”

Section: It Itmentioning

confidence: 99%

On certain point-countable covers

Burke¹,

Michael²

1976

Pacific J. Math.

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In recent years, there have been a number of results about spaces with a point-countable cover satisfying various assumptions. In this paper, these results are generalized and unified by showing that the assumptions used can be significantly weakened. We are mostly concerned with consequences of the following condition: There is a point-countable cover 3> of the space X such that, if JC, y G X with x ^ y, then 0> has a finite subcollection 9 such that x G (U 9)° and y £ U 9.

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“…According to a theorem of V. V. Filippov [9], every paracompact /»-space8 with a point-countable base is metrizable. Similarly, results of G. Creede [8], R. W. Heath [12] and R. H. Bing [4] imply that every cosmic space with a point-countable base is metrizable.…”

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confidence: 99%