synovial-joint
发表于 2025-3-26 23:56:09
The Countable Sum Theorem for Covering Dimension,In this chapter we prove two of the most important results for covering dimension, the countable sum theorem for normal spaces and the subset theorem for perfectly normal spaces. Both results are due to Čech.
带伤害
发表于 2025-3-27 03:47:28
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优雅
发表于 2025-3-27 05:27:14
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reception
发表于 2025-3-27 12:40:42
Coincidence, Product and Decomposition Theorems for Separable Metric Spaces,Let ., . be disjoint closed sets of a non-empty compact regular space . with .. Let . be a finite open cover of .. Then there are disjoint closed sets .., .. of . such that . and the trace of . on . ∖ (.. ∪ ..) has a finite open refinement . of order at most . − 1.
后天习得
发表于 2025-3-27 14:53:40
Axiomatic Characterization of the Dimension of Separable Metric Spaces,Consider the following axioms for a dimension function . on a class of spaces . that contains all Euclidean cubes . and every space that is homeomorphic to a subspace of a member of .. Bear in mind that by our definition of a dimension function, . if . and . are homeomorphic, and . iff . = ∅.
rectum
发表于 2025-3-27 20:43:08
Cozero Sets and Covering Dimension dim0,In this chapter we establish the fundamental properties of the dimension function dim. that was defined earlier in Chap. ., including the countable sum theorem and the subset theorem. We first recall some standard properties of zero and cozero sets.
沙发
发表于 2025-3-28 00:50:18
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ostrish
发表于 2025-3-28 03:20:26
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airborne
发表于 2025-3-28 07:31:01
Dimension Theory978-3-030-22232-1Series ISSN 1875-7634 Series E-ISSN 2215-1885
思考而得
发表于 2025-3-28 13:42:03
Jacques-Philippe Leyens,Benoit Dardenne to Morita and Smirnov, who generalized the result of Alexandroff for the case of compact Hausdorff spaces. From this inequality, the countable sum theorem for . and the Urysohn inequality for ., it will follow that . and ..