کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658445 | 1633099 | 2014 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Preservation and destruction in simple refinements
ترجمه فارسی عنوان
حفاظت و تخریب در تصحیح ساده
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
If Ï is a topology on X and AâX, we let ãÏ,Aã denote the topology generated by Ï and A, i.e., the topology with Ïâª{A} as a subbasis. Any refinement of a topology obtained like this - by declaring just one new set to be open - we call simple. The present paper investigates the preservation of various properties in simple refinements. The locally closed sets (sets open in their closure) play a crucial role here: it turns out that many properties are preserved in a simple refinement by A if and only if A is locally closed. We prove this for the properties of regularity, completely regularity, (complete) metrizability, and (complete) ultrametrizability. We also show that local compactness is preserved in a simple refinement by A if and only if both A and its complement are locally closed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 178, 1 December 2014, Pages 236-247
Journal: Topology and its Applications - Volume 178, 1 December 2014, Pages 236-247
نویسندگان
William R. Brian,