continuity - 2025 ACF Fall

Tossup

If both a bijection between topological spaces and its inverse (-5[1])have this property, (10[1])it is called (10[1])a homeomorphism. (10[7]-5[3])If a (10[1])function (10[1])scales the distance between two (10[1])points by at most a constant, (-5[1])it has a form of this property (10[2])named for Rudolf Lipschitz. (10[12]-5[1])A (10[1])function (10[3])has (10[1])this (10[3])property (10[3])if and only (10[1])if (10[1])the pre-image of any open set (-5[1])is itself open. (10[2])On an interval (10[1]-5[1])[a, b] (“a b”), a function f with this property will take (10[1])all values (10[1])between (10[5])[read slowly] f (10[4])of (10[3])a (10[5]-5[1])and (10[1])f (10[1])of (10[4])b (10[11]-5[2])by (10[1])the (10[3])intermediate (10[3])value theorem. (10[8]-5[1])A function (10[3])has this property (10[3])if it equals (10[1])its limit (10[4]-5[1])at every point. (10[3])For 10 points, (10[1])name (10[2])this (10[1])property of a (10[1])function (10[1])that can be defined (10[1])informally as being able to draw its graph (10[1])without (10[1])taking the pen off (10[1])the paper. (10[1])■END■ (10[6]0[1])

ANSWER: continuity [accept word forms such as continuous; accept uniformly continuous; accept uniform continuity; accept Lipschitz continuous; accept Lipschitz continuity]

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Buzzes

Player	Team	Opponent	Position	Value
Rishi Mathur	Claremont B	USC A	9	-5
Skand Parvatikar	Arizona State B	Texas	12	10
Taran Knutson	Michigan A	Michigan State C	15	10
Ty Brennan	Berkeley Mighty Miner	Stanford B	17	-5
Cliodora Selyuzhitsky	UCSD A	UCLA A	17	10
Chris Chang	USC A	Claremont B	17	10
Nameer Qadir	Toronto C	Waterloo A	17	10
Nate Brown	CWRU C	CWRU B	17	10
Oliver Thompson	CWRU D	Michigan State A	17	10
Liam Rojas	Virginia A	Virginia Tech A	17	-5
Daniel Abrams	Rutgers B	Maryland B	17	-5
Will Huang	Wisconsin A	Macalester	17	10
Oliver West	Cambridge B	Imperial C	17	10
Annika Larson	Claremont A	UCLA B	19	10
Aidan Keenan	Rochester	RIT A	20	10
Dmitri Anh-Minh Tran	UC Santa Barbara	UCLA F	25	10
Jesse Mindel	NCSU A	Virginia Tech B	31	-5
Aleksa Misic	Waterloo B	Toronto E	38	10
Eric Lipsutz	Chicago B	WashU Grizzlers	38	10
Anthony Gagliano	McGill A	Ottawa A	42	10
Samuel Zheng	Toronto F	Toronto H	42	10
Ryan Liu	Ohio State D	Louisville D	42	-5
Zachary Bornstein	Virginia Tech A	Virginia A	42	10
Zaid Asif	NYU A	George Mason B	42	10
Beckett Pursey	Purdue B	Indiana A	42	10
Camden Walker	WashU Grolars	Rose-Hulman A	42	10
Eames Weeks	Brown A	Tufts C	42	10
David Xilbille	Georgia Tech C	Tennessee A	42	10
Rufus Gladwell	Durham A	Durham B	42	10
Rob Morris	Durham D	Sheffield A	42	10
Antara Bhattacharya	Cambridge A	Southampton	42	10
Connor Yu	Cornell C	Cornell A	42	10
Anne Fjeld	Alberta A	British Columbia B	43	10
Tianyi Zheng	UCSD B	UCLA D	44	10
Jeremy Scurlock	Chipola College	Vanderbilt A	44	10
Michael Shipman	Cambridge D	Imperial A	44	10
Daniel Slater	Tennessee Tech	Auburn B	45	10
Joseph Wang	UCLA E	UC Irvine	46	10
Cranmer McGinn	McMaster C	Queen's A	46	10
James Xiao	Toronto A	McMaster A	46	10
Denali Tran-Le	McGill B	McGill C	47	10
Nikhil Nair	Boston University B	Brandeis Beethoven	47	10
Ryan Zhang	Washington State	Washington Pink	47	10
Elizabeth Bowling	Indiana B	Chicago A	50	10
Nathaniel Martin	Brandeis Bach	Williams C	51	10
Niki Ilia	Boston College B	Vermont A	57	-5
Madeline Strauss	Tufts A	UConn A	60	10
Jonathan Ho	Alberta B	Washington Masu	60	10
Aryan Malhotra	Rutgers C	NYU B	63	-5
Aeron Wheel	Cardiff	Bristol	63	10
Nathan Woolery	Louisville C	Michigan C	73	10
Michael Xu	McMaster B	Guelph A	75	10
Hansen Jin	Berkeley Skeleton King	Stanford A	76	10
Ezra Siegartel	Vassar B	Penn	76	10
Matthew Kohn	Williams A	Southern Connecticut State University A	76	10
James Zhao	Vanderbilt C	Mississippi State A	76	10
Ariyan Miah	Binghamton B	Cornell B	76	10
Aaryan Sumesh	Berkeley Archer Queen	Berkeley Boss Bandit	77	10
Anjali Rao	Ottawa B	Ottawa D	77	10
June Miller	Florida A	Florida Tech A	77	10
Nishad Joshi	Kentucky	Michigan State D	77	10
Alex Wong	Rutgers D	George Mason A	78	10
Advaith Jagannath	Cambridge C	Birmingham	78	10
Alex Forman	Cornell D	Binghamton A	78	10
Taman Truong	USC B	Claremont C	79	10
Connor King	St. Thomas	Iowa State	79	10
William Kiker	Dartmouth A	Amherst B	79	10
Wesley Stine	Clemson A	Alabama A	79	-5
Joanna Xiao	Georgia Tech B	Auburn A	79	10
Jolie Yeh	Warwick	LSE	79	10
Logan Van Pelt	Washington Coho	Washington Chinook	80	10
Sewanth Paudel	Ohio State C	Michigan State B	81	10
Saju Ramraj	Toronto I	Brock A	82	10
Ethan Ma	Illinois Blue	Illinois Canada	82	10
Jonathan Schnipper	Brandeis Mozart	Vermont B	82	10
Pen Hughes	Edinburgh C	Sheffield B	82	10
Lorie Au-Yeung	UCSC	Berkeley Little Prince	83	10
Gus Morin-Strom	Carleton B	McGill E	83	10
Will Marcotte	Toronto D	Toronto B	83	-5
Meredie Cohen	William & Mary A	UNC A	83	10
Brayden Whitlow	George Mason C	Stony Brook	83	10
Omer Korkmaz	Johns Hopkins	Columbia A	83	10
Johnathan Ahdout	Princeton	Maryland A	83	10
Ayaan Jajodia	Dartmouth B	Boston University A	83	-5
William Berger	Dartmouth C	MIT B	83	10
John Shelley	Clemson B	Tennessee B	83	10
Andrew Wilson	Montevallo	Clemson C	83	10
Sam Chernoff	Emory A	Georgia Tech F	83	10
Caleb Slusher	South Carolina A	Georgia Tech A	83	10
Asish Madarapu	UNC D	UNC C	84	10
David Ropp	Duke A	William & Mary B	85	10
Alex Dzurick	William Woods University A	Illinois Champaign	85	10
Arthur Zhang	Purdue C	Illinois Orange	85	10
Orin Overmiller	Florida Tech B	Florida State A	86	10
Cooper Morris	Columbia B	Rowan	86	10
Samarth Prajapati	Georgia Tech E	Georgia A	86	10
Brody Johnson	Louisville B	Louisville A	88	10
Andrew McKenzie	Ohio State B	Pittsburgh	88	10
Peter Zeng	Ohio State A	WVU B	88	10
Fern Fang	VCU A	Virginia Tech C	88	10
Gavin Chen	Vassar A	Rutgers A	88	10
Salil Jain	Williams B	Amherst A	88	10
Reid Eichberg	Tufts B	Boston College A	88	10
Matthew Bray	Auburn C	Vanderbilt B	88	10
Benjamin Turner	York	Edinburgh B	88	-5
Alden Thompson	Carleton A	Ottawa C	90	10
Nicholas Ryan	Lehigh B	NYU C	90	10
Rae Meyers	Arizona State A	British Columbia C	90	10
Matthew Andersen	Florida B	UCF A	93	10
Alex Grigoriades	Lehigh A	Maryland C	93	10
James Windle	Purdue D	Iowa B	93	10
Lucas Hall	Waterloo C	Toronto G	96	10
Levan Tsiskarisvili	JMU B	Liberty C	98	10
Ba Loc Dinh	Illinois Urbana	Iowa A	98	-5
Luke Sauer	Michigan Tech	Minnesota	98	10
Wesley Yu	British Columbia A	Washington Atlantic	98	10
Ahmed Azhari	Cambridge E	Oxford	98	10
Sai Subramanian	CWRU A	Michigan D	101	10
Cara Leonard	William & Mary C	JMU A	101	10
Andres Lorenzo	RIT B	ESF	101	10
Alex Hestermann	Washington Sockeye	Boise State	104	10
Yishak Kelkay	ERAU Daytona A	South Florida A	105	10
Nathan Sprouse	Virginia Tech B	NCSU A	105	10
Brady Bier	Boston University A	Dartmouth B	106	10
Rafa Travis	Durham C	Edinburgh A	109	10
Kevin Nolan	NCSU B	Tusculum A	110	10
Chris Wang	Toronto B	Toronto D	114	10
Daniel Huang	Georgia Tech D	Sewanne	122	10
Ollie Glin-Conway	Imperial D	Imperial B	123	10
Noah Lang	Wisconsin B	Wisconsin C	127	10
Grace Early	Iowa A	Illinois Urbana	129	10
Danny Han	Stanford B	Berkeley Mighty Miner	130	10
Bonham Buchannon	Louisville D	Ohio State D	130	10
Rohit Chintala	Maryland B	Rutgers B	130	10
Gabe Rosen-Turits	NYU B	Rutgers C	130	10
Cy Stavros	Vermont A	Boston College B	130	10
Jackson McDonald	Alabama A	Clemson A	130	10
Leona Barker	Edinburgh B	York	130	0

Summary

Tournament	Edition	TUH	Conv. %	Neg %	Average Buzz
UK (North)	UK	5	80%	20%	68.75
UK (South)	UK	8	100%	0%	68.00
Northern California	US	4	100%	25%	91.50
Southern California	US	7	100%	14%	35.29
Eastern Canada (1)	US	5	100%	0%	67.80
Eastern Canada (2)	US	9	100%	11%	61.78
Florida	US	4	100%	0%	90.25
Great Lakes	US	11	100%	9%	70.45
Lower Mid-Atlantic	US	9	100%	22%	88.44
Upper Mid-Atlantic	US	12	100%	17%	88.50
Midwest	US	9	100%	11%	71.78
North	US	4	100%	0%	80.25
Northeast	US	12	100%	17%	77.67
Pacific	US	8	100%	0%	66.75
Southeast	US	13	100%	8%	80.31
Upstate NY	US	5	100%	0%	63.40